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Sample records for banach space

  1. Isometries on Banach spaces function spaces

    CERN Document Server

    Fleming, Richard J

    2002-01-01

    Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise, Banach showed that every linear isometry on the space of continuous functions on a compact metric space must transform a continuous function x into a continuous function y satisfying y(t) = h(t)x(p(t)), where p is a homeomorphism and |h| is identically one.Isometries on Banach Spaces: Function Spaces is the first of two planned volumes that survey investigations of Banach-space isometries. This volume emphasizes the characterization of isometries and focuses on establishing the type of explicit, canonical form given above in a variety of settings. After an introductory discussion of isometries in general, four chapters are devoted to describing the isometries on classical function spaces. The final chapter explores isometries on Banach algebras.This treatment p...

  2. Banach spaces of continuous functions as dual spaces

    CERN Document Server

    Dales, H G; Lau, A T -M; Strauss, D

    2016-01-01

    This book gives a coherent account of the theory of Banach spaces and Banach lattices, using the spaces C_0(K) of continuous functions on a locally compact space K as the main example. The study of C_0(K) has been an important area of functional analysis for many years. It gives several new constructions, some involving Boolean rings, of this space as well as many results on the Stonean space of Boolean rings. The book also discusses when Banach spaces of continuous functions are dual spaces and when they are bidual spaces.

  3. Topics in Banach space theory

    CERN Document Server

    Albiac, Fernando

    2016-01-01

    This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous f...

  4. On Uniformly finitely extensible Banach spaces

    OpenAIRE

    Castillo, Jesús M. F.; Ferenczi, Valentin; Moreno, Yolanda

    2013-01-01

    We continue the study of Uniformly Finitely Extensible Banach spaces (in short, UFO) initiated in Moreno-Plichko, \\emph{On automorphic Banach spaces}, Israel J. Math. 169 (2009) 29--45 and Castillo-Plichko, \\emph{Banach spaces in various positions.} J. Funct. Anal. 259 (2010) 2098-2138. We show that they have the Uniform Approximation Property of Pe\\l czy\\'nski and Rosenthal and are compactly extensible. We will also consider their connection with the automorphic space problem of Lindenstraus...

  5. On Λ-Type Duality of Frames in Banach Spaces

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    Renu Chugh

    2013-11-01

    Full Text Available Frames are redundant system which are useful in the reconstruction of certain classes of spaces. The dual of a frame (Hilbert always exists and can be obtained in a natural way. Due to the presence of three Banach spaces in the definition of retro Banach frames (or Banach frames duality of frames in Banach spaces is not similar to frames for Hilbert spaces. In this paper we introduce the notion of Λ-type duality of retro Banach frames. This can be generalized to Banach frames in Banach spaces. Necessary and sufficient conditions for the existence of the dual of retro Banach frames are obtained. A special class of retro Banach frames which always admit a dual frame is discussed.

  6. Computable Frames in Computable Banach Spaces

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    S.K. Kaushik

    2016-06-01

    Full Text Available We develop some parts of the frame theory in Banach spaces from the point of view of Computable Analysis. We define computable M-basis and use it to construct a computable Banach space of scalar valued sequences. Computable Xd frames and computable Banach frames are also defined and computable versions of sufficient conditions for their existence are obtained.

  7. Interpolation of quasi-Banach spaces

    International Nuclear Information System (INIS)

    Tabacco Vignati, A.M.

    1986-01-01

    This dissertation presents a method of complex interpolation for familities of quasi-Banach spaces. This method generalizes the theory for families of Banach spaces, introduced by others. Intermediate spaces in several particular cases are characterized using different approaches. The situation when all the spaces have finite dimensions is studied first. The second chapter contains the definitions and main properties of the new interpolation spaces, and an example concerning the Schatten ideals associated with a separable Hilbert space. The case of L/sup P/ spaces follows from the maximal operator theory contained in Chapter III. Also introduced is a different method of interpolation for quasi-Banach lattices of functions, and conditions are given to guarantee that the two techniques yield the same result. Finally, the last chapter contains a different, and more direct, approach to the case of Hardy spaces

  8. Analysis in Banach spaces

    CERN Document Server

    Hytönen, Tuomas; Veraar, Mark; Weis, Lutz

    The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes. The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional an...

  9. Spear operators between Banach spaces

    CERN Document Server

    Kadets, Vladimir; Merí, Javier; Pérez, Antonio

    2018-01-01

    This monograph is devoted to the study of spear operators, that is, bounded linear operators $G$ between Banach spaces $X$ and $Y$ satisfying that for every other bounded linear operator $T:X\\longrightarrow Y$ there exists a modulus-one scalar $\\omega$ such that $\\|G + \\omega\\,T\\|=1+ \\|T\\|$. This concept extends the properties of the identity operator in those Banach spaces having numerical index one. Many examples among classical spaces are provided, being one of them the Fourier transform on $L_1$. The relationships with the Radon-Nikodým property, with Asplund spaces and with the duality, and some isometric and isomorphic consequences are provided. Finally, Lipschitz operators satisfying the Lipschitz version of the equation above are studied. The book could be of interest to young researchers and specialists in functional analysis, in particular to those interested in Banach spaces and their geometry. It is essentially self-contained and only basic knowledge of functional analysis is needed.

  10. Open problems in Banach spaces and measure theory | Rodríguez ...

    African Journals Online (AJOL)

    We collect several open questions in Banach spaces, mostly related to measure theoretic aspects of the theory. The problems are divided into five categories: miscellaneous problems in Banach spaces (non-separable Lp spaces, compactness in Banach spaces, w*-null sequences in dual spaces), measurability in Banach ...

  11. Topology, isomorphic smoothness and polyhedrality in Banach spaces

    OpenAIRE

    Smith, Richard J.

    2018-01-01

    In recent decades, topology has come to play an increasing role in some geometric aspects of Banach space theory. The class of so-called $w^*$-locally relatively compact sets was introduced recently by Fonf, Pallares, Troyanski and the author, and were found to be a useful topological tool in the theory of isomorphic smoothness and polyhedrality in Banach spaces. We develop the topological theory of these sets and present some Banach space applications.

  12. Banach frames for multivariate alpha-modulation spaces

    DEFF Research Database (Denmark)

    Borup, Lasse; Nielsen, Morten

    2006-01-01

    The α-modulation spaces [$Mathematical Term$], form a family of spaces that include the Besov and modulation spaces as special cases. This paper is concerned with construction of Banach frames for α-modulation spaces in the multivariate setting. The frames constructed are unions of independent Ri...... Riesz sequences based on tensor products of univariate brushlet functions, which simplifies the analysis of the full frame. We show that the multivariate α-modulation spaces can be completely characterized by the Banach frames constructed....

  13. Quantitative Hahn-Banach Theorems and Isometric Extensions forWavelet and Other Banach Spaces

    Directory of Open Access Journals (Sweden)

    Sergey Ajiev

    2013-05-01

    Full Text Available We introduce and study Clarkson, Dol’nikov-Pichugov, Jacobi and mutual diameter constants reflecting the geometry of a Banach space and Clarkson, Jacobi and Pichugov classes of Banach spaces and their relations with James, self-Jung, Kottman and Schäffer constants in order to establish quantitative versions of Hahn-Banach separability theorem and to characterise the isometric extendability of Hölder-Lipschitz mappings. Abstract results are further applied to the spaces and pairs from the wide classes IG and IG+ and non-commutative Lp-spaces. The intimate relation between the subspaces and quotients of the IG-spaces on one side and various types of anisotropic Besov, Lizorkin-Triebel and Sobolev spaces of functions on open subsets of an Euclidean space defined in terms of differences, local polynomial approximations, wavelet decompositions and other means (as well as the duals and the lp-sums of all these spaces on the other side, allows us to present the algorithm of extending the main results of the article to the latter spaces and pairs. Special attention is paid to the matter of sharpness. Our approach is quasi-Euclidean in its nature because it relies on the extrapolation of properties of Hilbert spaces and the study of 1-complemented subspaces of the spaces under consideration.

  14. Simultaneous approximation in scales of Banach spaces

    International Nuclear Information System (INIS)

    Bramble, J.H.; Scott, R.

    1978-01-01

    The problem of verifying optimal approximation simultaneously in different norms in a Banach scale is reduced to verification of optimal approximation in the highest order norm. The basic tool used is the Banach space interpolation method developed by Lions and Peetre. Applications are given to several problems arising in the theory of finite element methods

  15. A strong open mapping theorem for surjections from cones onto Banach spaces

    NARCIS (Netherlands)

    Jeu, de M.F.E.; Messerschmidt, H.J.M.

    2014-01-01

    We show that a continuous additive positively homogeneous map from a closed not necessarily proper cone in a Banach space onto a Banach space is an open map precisely when it is surjective. This generalization of the usual Open Mapping Theorem for Banach spaces is then combined with Michael's

  16. Fixed Points of Expansive Type Mappings in 2-Banach Spaces

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    Prabha Chouhan

    2013-08-01

    Full Text Available In present paper, we define expansive mappings in 2-Banach space and prove some common unique fixed point theorems which are the extension of results of Wang et al. [12] and Rhoades [9] in 2-Banach space.

  17. (s, μ)-similar operators in the Banach spaces

    International Nuclear Information System (INIS)

    Samarskij, V.G.

    1978-01-01

    The theory of the operator ideals formed by means of S function is developed. The problem of the construction of the operator acting from one Banach space to another whose S numbers are near to the given ones, is solved. Several conditions, sufficient for that any wholly continuous operator in the Gilbert space were transferred to the given pair of the Banach spaces without distorting too much the values of its S-numbers, are given. All the considered operators are assumed to be linear and continuous ones

  18. Open problems in the geometry and analysis of Banach spaces

    CERN Document Server

    Guirao, Antonio J; Zizler, Václav

    2016-01-01

    This is a collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help convince young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems presented herein are longstanding open problems, some are recent, some are more important and some are only "local" problems. Some would ...

  19. Second order evolution inclusions governed by sweeping process in Banach spaces

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    A. G. Ibrahim

    2009-11-01

    Full Text Available In this paper we prove two existence theorems concerning the existence of solutions for second order evolution inclusions governed by sweeping process with closed convex sets depending on time and state in Banach spaces. This work extends some recent existence theorems cncerning sweeping process from Hilbert spaces to Banach spaces.

  20. Banach spaces that realize minimal fillings

    International Nuclear Information System (INIS)

    Bednov, B. B.; Borodin, P. A.

    2014-01-01

    It is proved that a real Banach space realizes minimal fillings for all its finite subsets (a shortest network spanning a fixed finite subset always exists and has the minimum possible length) if and only if it is a predual of L 1 . The spaces L 1 are characterized in terms of Steiner points (medians). Bibliography: 25 titles. (paper)

  1. Minimal and Maximal Operator Space Structures on Banach Spaces

    OpenAIRE

    P., Vinod Kumar; Balasubramani, M. S.

    2014-01-01

    Given a Banach space $X$, there are many operator space structures possible on $X$, which all have $X$ as their first matrix level. Blecher and Paulsen identified two extreme operator space structures on $X$, namely $Min(X)$ and $Max(X)$ which represents respectively, the smallest and the largest operator space structures admissible on $X$. In this note, we consider the subspace and the quotient space structure of minimal and maximal operator spaces.

  2. Submonotone mappings in Banach spaces and applications

    International Nuclear Information System (INIS)

    Georgiev, P.G.

    1995-11-01

    The notions 'submonotone' and 'strictly submonotone' mapping, introduced by J. Spingarn in R n , are extended in a natural way to arbitrary Banach spaces. Several results about monotone operators are proved for submonotone and strictly submonotone ones: Rockafellar's result about local boundedness of monotone operators; Kenderov's result about single-valuedness and upper-semicontinuity almost everywhere of monotone operators in Asplund spaces; minimality (as w * - cusco mappings) of maximal strictly submonotone mappings, etc. It is shown that subdifferentials of various classes non-convex functions defined as pointwise suprema of quasi-differentiable functions possess submonotone properties. Results about generic differentiability of such functions are obtained (among them are new generalizations of an Ekeland and Lebourg's theorem). Applications are given to the properties of the distance function in a Banach space with uniformly Gateaux differentiable norm. (author). 29 refs

  3. FOREWORD: Tackling inverse problems in a Banach space environment: from theory to applications Tackling inverse problems in a Banach space environment: from theory to applications

    Science.gov (United States)

    Schuster, Thomas; Hofmann, Bernd; Kaltenbacher, Barbara

    2012-10-01

    Inverse problems can usually be modelled as operator equations in infinite-dimensional spaces with a forward operator acting between Hilbert or Banach spaces—a formulation which quite often also serves as the basis for defining and analyzing solution methods. The additional amount of structure and geometric interpretability provided by the concept of an inner product has rendered these methods amenable to a convergence analysis, a fact which has led to a rigorous and comprehensive study of regularization methods in Hilbert spaces over the last three decades. However, for numerous problems such as x-ray diffractometry, certain inverse scattering problems and a number of parameter identification problems in PDEs, the reasons for using a Hilbert space setting seem to be based on conventions rather than an appropriate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, non-Hilbertian regularization and data fidelity terms incorporating a priori information on solution and noise, such as general Lp-norms, TV-type norms, or the Kullback-Leibler divergence, have recently become very popular. These facts have motivated intensive investigations on regularization methods in Banach spaces, a topic which has emerged as a highly active research field within the area of inverse problems. Meanwhile some of the most well-known regularization approaches, such as Tikhonov-type methods requiring the solution of extremal problems, and iterative ones like the Landweber method, the Gauss-Newton method, as well as the approximate inverse method, have been investigated for linear and nonlinear operator equations in Banach spaces. Convergence with rates has been proven and conditions on the solution smoothness and on the structure of nonlinearity have been formulated. Still, beyond the existing results a large number of challenging open questions have arisen, due to the more involved handling of general Banach spaces and the larger variety

  4. Regularization methods in Banach spaces

    CERN Document Server

    Schuster, Thomas; Hofmann, Bernd; Kazimierski, Kamil S

    2012-01-01

    Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Usually the mathematical model of an inverse problem consists of an operator equation of the first kind and often the associated forward operator acts between Hilbert spaces. However, for numerous problems the reasons for using a Hilbert space setting seem to be based rather on conventions than on an approprimate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, sparsity constraints using general Lp-norms or the B

  5. Functional Equations in Fuzzy Banach Spaces

    Directory of Open Access Journals (Sweden)

    M. Eshaghi Gordji

    2012-01-01

    generalized Hyers-Ulam stability of the following additive-quadratic functional equation f(x+ky+f(x−ky=f(x+y+f(x−y+(2(k+1/kf(ky−2(k+1f(y for fixed integers k with k≠0,±1 in fuzzy Banach spaces.

  6. The approximate inverse in action: IV. Semi-discrete equations in a Banach space setting

    International Nuclear Information System (INIS)

    Schuster, T; Schöpfer, F; Rieder, A

    2012-01-01

    This article concerns the method of approximate inverse to solve semi-discrete, linear operator equations in Banach spaces. Semi-discrete means that we search for a solution in an infinite-dimensional Banach space having only a finite number of data available. In this sense the situation is applicable to a large variety of applications where a measurement process delivers a discretization of an infinite-dimensional data space. The method of approximate inverse computes scalar products of the data with pre-computed reconstruction kernels which are associated with mollifiers and the dual of the model operator. The convergence, approximation power and regularization property of this method when applied to semi-discrete operator equations in Hilbert spaces has been investigated in three prequels to this paper. Here we extend these results to a Banach space setting. We prove convergence and stability for general Banach spaces and reproduce the results specifically for the integration operator acting on the space of continuous functions. (paper)

  7. On Uniform Exponential Trichotomy in Banach Spaces

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    Kovacs Monteola Ilona

    2014-06-01

    Full Text Available In this paper we consider three concepts of uniform exponential trichotomy on the half-line in the general framework of evolution operators in Banach spaces. We obtain a systematic classification of uniform exponential trichotomy concepts and the connections between them.

  8. The Maslov index in symplectic Banach spaces

    CERN Document Server

    Booss-Bavnbek, Bernhelm

    2018-01-01

    The authors consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying weak symplectic structures. Assuming vanishing index, they obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using such decompositions the authors define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. The authors prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction while recovering all the standard properties of the Maslov index. As an application, the authors consider curves of elliptic operators which have varying principal symbol, varying maximal domain and are not necessarily of Dirac type. For this class of operator curves, the authors derive a desuspension spectral flow formula for varying well-posed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral f...

  9. A Hilbert space structure on Banach algebras

    International Nuclear Information System (INIS)

    Mohammad, N.; Thaheem, A.B.

    1988-08-01

    In this note we define an inner product on ''reduced'' Banach *-algebras via a measure on the set of positive functionals. It is shown here that the resultant inner product space is a topological algebra and also a completeness condition is obtained. (author). 9 refs

  10. Homomorphisms and functional calculus on algebras on entire functions on Banach spaces

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    H. M. Pryimak

    2015-07-01

    Full Text Available The paper is devoted to study homomorphisms of algebras of entire functionson Banach spaces to a commutative Banach algebra. In particular, it is proposed amethod to construct homomorphisms vanishing on homogeneouspolynomials of degree less or equal that a fixed number $n.$

  11. Ito's formula in UMD Banach spaces and regularity of solution of the Zakai equation

    NARCIS (Netherlands)

    Brzezniak, Z.; Van Neerven, J.M.A.M.; Veraar, M.C.; Weis, L.

    2008-01-01

    Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Itô formula is proved which is applied to prove the existence of strong solutions for a class of stochastic evolution equations in UMD Banach spaces. The abstract results

  12. Greedy Algorithms for Reduced Bases in Banach Spaces

    KAUST Repository

    DeVore, Ronald

    2013-02-26

    Given a Banach space X and one of its compact sets F, we consider the problem of finding a good n-dimensional space X n⊂X which can be used to approximate the elements of F. The best possible error we can achieve for such an approximation is given by the Kolmogorov width dn(F)X. However, finding the space which gives this performance is typically numerically intractable. Recently, a new greedy strategy for obtaining good spaces was given in the context of the reduced basis method for solving a parametric family of PDEs. The performance of this greedy algorithm was initially analyzed in Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) in the case X=H is a Hilbert space. The results of Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) were significantly improved upon in Binev et al. (SIAM J. Math. Anal. 43:1457-1472, 2011). The purpose of the present paper is to give a new analysis of the performance of such greedy algorithms. Our analysis not only gives improved results for the Hilbert space case but can also be applied to the same greedy procedure in general Banach spaces. © 2013 Springer Science+Business Media New York.

  13. Introduction to Banach spaces and algebras

    CERN Document Server

    Allan, Graham

    2010-01-01

    Banach spaces and algebras are a key topic of pure mathematics. Graham Allan's careful and detailed introductory account will prove essential reading for anyone wishing to specialise in functional analysis and is aimed at final year undergraduates or masters level students. Based on the author's lectures to fourth year students at Cambridge University, the book assumes knowledge typical of first degrees in mathematics, including metric spaces, analytic topology, and complexanalysis. However, readers are not expected to be familiar with the Lebesgue theory of measure and integration.The text be

  14. Polynomials and identities on real Banach spaces

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr Pavel; Kraus, M.

    2012-01-01

    Roč. 385, č. 2 (2012), s. 1015-1026 ISSN 0022-247X R&D Projects: GA ČR(CZ) GAP201/11/0345 Institutional research plan: CEZ:AV0Z10190503 Keywords : Polynomials on Banach spaces Subject RIV: BA - General Mathematics Impact factor: 1.050, year: 2012 http://www.sciencedirect.com/science/article/pii/S0022247X11006743

  15. Geometric properties of Banach spaces and nonlinear iterations

    CERN Document Server

    Chidume, Charles

    2009-01-01

    Nonlinear functional analysis and applications is an area of study that has provided fascination for many mathematicians across the world. This monograph delves specifically into the topic of the geometric properties of Banach spaces and nonlinear iterations, a subject of extensive research over the past thirty years. Chapters 1 to 5 develop materials on convexity and smoothness of Banach spaces, associated moduli and connections with duality maps. Key results obtained are summarized at the end of each chapter for easy reference. Chapters 6 to 23 deal with an in-depth, comprehensive and up-to-date coverage of the main ideas, concepts and results on iterative algorithms for the approximation of fixed points of nonlinear nonexpansive and pseudo-contractive-type mappings. This includes detailed workings on solutions of variational inequality problems, solutions of Hammerstein integral equations, and common fixed points (and common zeros) of families of nonlinear mappings. Carefully referenced and full of recent,...

  16. Phaseless tomographic inverse scattering in Banach spaces

    International Nuclear Information System (INIS)

    Estatico, C.; Fedeli, A.; Pastorino, M.; Randazzo, A.; Tavanti, E.

    2016-01-01

    In conventional microwave imaging, a hidden dielectric object under test is illuminated by microwave incident waves and the field it scatters is measured in magnitude and phase in order to retrieve the dielectric properties by solving the related non-homogenous Helmholtz equation or its Lippmann-Schwinger integral formulation. Since the measurement of the phase of electromagnetic waves can be still considered expensive in real applications, in this paper only the magnitude of the scattering wave fields is measured in order to allow a reduction of the cost of the measurement apparatus. In this respect, we firstly analyse the properties of the phaseless scattering nonlinear forward modelling operator in its integral form and we provide an analytical expression for computing its Fréchet derivative. Then, we propose an inexact Newton method to solve the associated nonlinear inverse problems, where any linearized step is solved by a L p Banach space iterative regularization method which acts on the dual space L p* . Indeed, it is well known that regularization in special Banach spaces, such us L p with 1 < p < 2, allows to promote sparsity and to reduce Gibbs phenomena and over-smoothness. Preliminary results concerning numerically computed field data are shown. (paper)

  17. The Multivariate Müntz-Szasz Problem in Weighted Banach Space on Rn

    Directory of Open Access Journals (Sweden)

    Xiangdong Yang

    2014-01-01

    Full Text Available The purpose of this paper is to give an extension of Müntz-Szasz theorems to multivariable weighted Banach space. Denote by {λk=(λk1,λk2,...,λkn}k=1∞ a sequence of real numbers in R+n. The completeness of monomials {tλk} in Cα is investigated, where Cα is the weighted Banach spaces which consist of complex continuous functions f defined on Rn with f(t exp(-α(t vanishing at infinity in the uniform norm.

  18. Calculus Rules for V-Proximal Subdifferentials in Smooth Banach Spaces

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    Messaoud Bounkhel

    2016-01-01

    Full Text Available In 2010, Bounkhel et al. introduced new proximal concepts (analytic proximal subdifferential, geometric proximal subdifferential, and proximal normal cone in reflexive smooth Banach spaces. They proved, in p-uniformly convex and q-uniformly smooth Banach spaces, the density theorem for the new concepts of proximal subdifferential and various important properties for both proximal subdifferential concepts and the proximal normal cone concept. In this paper, we establish calculus rules (fuzzy sum rule and chain rule for both proximal subdifferentials and we prove the Bishop-Phelps theorem for the proximal normal cone. The limiting concept for both proximal subdifferentials and for the proximal normal cone is defined and studied. We prove that both limiting constructions coincide with the Mordukhovich constructions under some assumptions on the space. Applications to nonconvex minimisation problems and nonconvex variational inequalities are established.

  19. Strictly diagonal holomorphic functions on Banach spaces

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    O. I. Fedak

    2016-01-01

    Full Text Available In this paper we investigate the boundedness of holomorphic functionals on a Banach space with a normalized basis $\\{e_n\\}$ which have a very special form $f(x=f(0+\\sum_{n=1}^\\infty c_nx_n^n$ and which we call strictly diagonal. We consider under which conditions strictly diagonal functions are entire and uniformly continuous on every ball of a fixed radius.

  20. Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces

    Directory of Open Access Journals (Sweden)

    Messaoud Bounkhel

    2013-01-01

    Full Text Available In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, ẋ(t∈F(t,x(t a.e. on I, x(t∈S, ∀t∈I, x(0=x0∈S, (*, where S is a closed subset in a Banach space , I=[0,T], (T>0, F:I×S→, is an upper semicontinuous set-valued mapping with convex values satisfying F(t,x⊂c(tx+xp, ∀(t,x∈I×S, where p∈ℝ, with p≠1, and c∈C([0,T],ℝ+. The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces.

  1. Iterative approximation of a solution of a general variational-like inclusion in Banach spaces

    International Nuclear Information System (INIS)

    Chidume, C.E.; Kazmi, K.R.; Zegeye, H.

    2002-07-01

    In this paper, we introduce a class of η-accretive mappings in a real Banach space, and show that the η-proximal point mapping for η-m-accretive mapping is Lipschitz continuous. Further we develop an iterative algorithm for a class of general variational-like inclusions involving η-accretive mappings in real Banach space, and discuss its convergence criteria. The class of η-accretive mappings includes several important classes of operators that have been studied by various authors. (author)

  2. Universal Birkhoff intergrabIility in dual Banach spaces | Rodr& ...

    African Journals Online (AJOL)

    We show that some classical results on universal Pettis integrability in dual Banach spaces can be formulated in terms of the Birkhoff integral, thanks to the link between Birkhoff integrability and the Bourgain property. Keywords: Birkhoff integral; Pettis integral; Bourgain property. Quaestiones Mathematicae 28(2005), 525– ...

  3. Fast regularizing sequential subspace optimization in Banach spaces

    International Nuclear Information System (INIS)

    Schöpfer, F; Schuster, T

    2009-01-01

    We are concerned with fast computations of regularized solutions of linear operator equations in Banach spaces in case only noisy data are available. To this end we modify recently developed sequential subspace optimization methods in such a way that the therein employed Bregman projections onto hyperplanes are replaced by Bregman projections onto stripes whose width is in the order of the noise level

  4. Weak compactness and sigma-Asplund generated Banach spaces

    Czech Academy of Sciences Publication Activity Database

    Fabian, Marián; Montesinos, V.; Zizler, Václav

    2007-01-01

    Roč. 181, č. 2 (2007), s. 125-152 ISSN 0039-3223 R&D Projects: GA AV ČR IAA1019301; GA AV ČR(CZ) IAA100190610 Institutional research plan: CEZ:AV0Z10190503 Keywords : epsilon-Asplund set * epsilon-weakly compact set * weakly compactly generated Banach space Subject RIV: BA - General Mathematics Impact factor: 0.568, year: 2007

  5. N-th order impulsive integro-differential equations in Banach spaces

    Directory of Open Access Journals (Sweden)

    Manfeng Hu

    2004-03-01

    Full Text Available We investigate the maximal and minimal solutions of initial value problem for N-th order nonlinear impulsive integro-differential equation in Banach space by establishing a comparison result and using the upper and lower solutions methods.

  6. A new differential calculus on a complex banach space with application to variational problems of quantum theory

    International Nuclear Information System (INIS)

    Sharma, C.S.; Rebelo, I.

    1975-01-01

    It is proved that a semilinear function on a complex banach space is not differentiable according to the usual definition of differentiability in the calculus on banch spaces. It is shown that this result makes the calculus largely inapplicable to the solution od variational problems of quantum mechanics. A new concept of differentiability called semidifferentiability is defined. This generalizes the standard concept of differentiability in a banach space and the resulting calculus is particularly suitable for optimizing real-value functions on a complex banach space and is directly applicable to the solution of quantum mechanical variational problems. As an example of such application a rigorous proof of a generalized version of a result due to Sharma (J. Phys. A; 2:413 (1969)) is given. In the course of this work a new concept of prelinearity is defined and some standard results in the calculus in banach spaces are extended and generalized into more powerful ones applicable directly to prelinear functions and hence yielding the standard results for linear function as particular cases. (author)

  7. STRICT CONVEXITY THROUGH EQUIVALENT NORMS IN SEPARABLES BANACH SPACES

    Directory of Open Access Journals (Sweden)

    Willy Zubiaga Vera

    2016-12-01

    Full Text Available Let E be a separable Banach space with norm || . ||. In the present work, the objective is to construct a norm || . ||1 that is equivalent to || . || in E, such that || . ||1 is strictly convex. In addition it is shown that its dual conjugate norm is also strictly convex.

  8. On the Fonte structure between a pair of Banach spaces

    International Nuclear Information System (INIS)

    Sharma, C.S.

    1990-01-01

    The main purpose of the present note is to establish the essential equivalence of the adjoint of a semilinear map defined through the Fonte structure between a pair of Banach spaces and the adjoint of the same map defined by Pian and the present author

  9. Convergence theorems for Banach space valued integrable multifunctions

    Directory of Open Access Journals (Sweden)

    Nikolaos S. Papageorgiou

    1987-01-01

    Full Text Available In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces LXP(Ω (1≤p≤∞. Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.

  10. The reconstruction property in Banach spaces and a perturbation theorem

    DEFF Research Database (Denmark)

    Casazza, P.G.; Christensen, Ole

    2008-01-01

    Perturbation theory is a fundamental tool in Banach space theory. However, the applications of the classical results are limited by the fact that they force the perturbed sequence to be equivalent to the given sequence. We will develop a more general perturbation theory that does not force...

  11. Periodic and almost periodic solutions for multi-valued differential equations in Banach spaces

    Directory of Open Access Journals (Sweden)

    E. Hanebaly

    2000-03-01

    Full Text Available It is known that for $omega$-periodic differential equations of monotonous type, in uniformly convex Banach spaces, the existence of a bounded solution on ${Bbb R}^+$ is equivalent to the existence of an omega-periodic solution (see Haraux [5] and Hanebaly [7, 10]. It is also known that if the Banach space is strictly convex and the equation is almost periodic and of monotonous type, then the existence of a continuous solution with a precompact range is equivalent to the existence of an almost periodic solution (see Hanebaly [8]. In this note we want to generalize the results above for multi-valued differential equations.

  12. Bounded and Periodic Solutions of Semilinear Impulsive Periodic System on Banach Spaces

    Directory of Open Access Journals (Sweden)

    Wei W

    2008-01-01

    Full Text Available Abstract A class of semilinear impulsive periodic system on Banach spaces is considered. First, we introduce the -periodic PC-mild solution of semilinear impulsive periodic system. By virtue of Gronwall lemma with impulse, the estimate on the PC-mild solutions is derived. The continuity and compactness of the new constructed Poincaré operator determined by impulsive evolution operator corresponding to homogenous linear impulsive periodic system are shown. This allows us to apply Horn's fixed-point theorem to prove the existence of -periodic PC-mild solutions when PC-mild solutions are ultimate bounded. This extends the study on periodic solutions of periodic system without impulse to periodic system with impulse on general Banach spaces. At last, an example is given for demonstration.

  13. Inexact Newton–Landweber iteration for solving nonlinear inverse problems in Banach spaces

    International Nuclear Information System (INIS)

    Jin, Qinian

    2012-01-01

    By making use of duality mappings, we formulate an inexact Newton–Landweber iteration method for solving nonlinear inverse problems in Banach spaces. The method consists of two components: an outer Newton iteration and an inner scheme providing the increments by applying the Landweber iteration in Banach spaces to the local linearized equations. It has the advantage of reducing computational work by computing more cheap steps in each inner scheme. We first prove a convergence result for the exact data case. When the data are given approximately, we terminate the method by a discrepancy principle and obtain a weak convergence result. Finally, we test the method by reporting some numerical simulations concerning the sparsity recovery and the noisy data containing outliers. (paper)

  14. Continuous local martingales and stochastic integration in UMD Banach spaces

    NARCIS (Netherlands)

    Veraar, M.C.

    2007-01-01

    Recently, van Neerven, Weis and the author, constructed a theory for stochastic integration of UMD Banach space valued processes. Here the authors use a (cylindrical) Brownian motion as an integrator. In this note we show how one can extend these results to the case where the integrator is an

  15. On some impulsive fractional differential equations in Banach spaces

    Directory of Open Access Journals (Sweden)

    JinRong Wang

    2010-01-01

    Full Text Available This paper deals with some impulsive fractional differential equations in Banach spaces. Utilizing the Leray-Schauder fixed point theorem and the impulsive nonlinear singular version of the Gronwall inequality, the existence of \\(PC\\-mild solutions for some fractional differential equations with impulses are obtained under some easily checked conditions. At last, an example is given for demonstration.

  16. Asymptotic behaviour of unbounded non expansive sequences in Banach spaces

    International Nuclear Information System (INIS)

    Djafari Rouhani, B.

    1990-08-01

    Let x be a real Banach space and C a subset of x. We consider a non expansive map t from an arbitrary subset C of x into itself, and for x is an element of C, we study the asymptotic behaviour of the sequence x T x n in x. 20 refs

  17. Some problems on ordinary differential equations in Banach spaces

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr Pavel; Vivi, P.

    2010-01-01

    Roč. 104, č. 2 (2010), s. 245-255 ISSN 1578-7303 R&D Projects: GA AV ČR IAA100190801; GA ČR GA201/07/0394 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach space * ODE * Peano's theorem Subject RIV: BA - General Mathematics Impact factor: 0.400, year: 2010 http://link.springer.com/article/10.5052%2FRACSAM.2010.16

  18. Fixed point iterations for quasi-contractive maps in uniformly smooth Banach spaces

    International Nuclear Information System (INIS)

    Chidume, C.E.; Osilike, M.O.

    1992-05-01

    Two well-known fixed point iteration methods are applied to approximate fixed points of quasi-contractive maps in real uniformly smooth Banach spaces. While our theorems generalize important known results, our method is of independent interest. (author). 25 refs

  19. Existence of zeros for operators taking their values in the dual of a Banach space

    Directory of Open Access Journals (Sweden)

    Ricceri Biagio

    2004-01-01

    Full Text Available Using continuous selections, we establish some existence results about the zeros of weakly continuous operators from a paracompact topological space into the dual of a reflexive real Banach space.

  20. A new class of Banach spaces

    International Nuclear Information System (INIS)

    Gill, T L; Zachary, W W

    2008-01-01

    In this paper, we construct a new class of separable Banach spaces KS p , for 1 ≤ p ≤ ∞, each of which contains all of the standard L p spaces, as well as the space of finitely additive measures, as compact dense embeddings. Equally important is the fact that these spaces contain all Henstock-Kurzweil integrable functions and, in particular, the Feynman kernel and the Dirac measure, as norm bounded elements. As a first application, we construct the elementary path integral in the manner originally intended by Feynman. We then suggest that KS 2 is a more appropriate Hilbert space for quantum theory, in that it satisfies the requirements for the Feynman, Heisenberg and Schroedinger representations, while the conventional choice only satisfies the requirements for the Heisenberg and Schroedinger representations. As a second application, we show that the mixed topology on the space of bounded continuous functions, C b [R n ], used to define the weak generator for a semigroup T(t), is stronger than the norm topology on KS p . (This means that, when extended to KS p , T(t) is strongly continuous, so that the weak generator on C b [R n ] becomes a strong generator on KS p .)

  1. Geometry and Gâteaux smoothness in separable Banach spaces

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr Pavel; Montesinos, V.; Zizler, Václav

    2012-01-01

    Roč. 6, č. 2 (2012), s. 201-232 ISSN 1846-3886 R&D Projects: GA ČR(CZ) GAP201/11/0345; GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : Gâteaux differentiable norms * extreme points * Radon -Nikodým property Subject RIV: BA - General Mathematics Impact factor: 0.529, year: 2012 http://oam.ele-math.com/06-15/Geometry-and-Gateaux-smoothness-in-separable-Banach-spaces

  2. Conical square function estimates in UMD Banach spaces and applications to H?-functional calculi

    NARCIS (Netherlands)

    Hytönen, T.; Van Neerven, J.; Portal, P.

    2008-01-01

    We study conical square function estimates for Banach-valued functions and introduce a vector-valued analogue of the Coifman-Meyer-Stein tent spaces. Following recent work of Auscher-M(c)Intosh-Russ, the tent spaces in turn are used to construct a scale of vector-valued Hardy spaces associated with

  3. Controllability of impulsive neutral functional differential inclusions with infinite delay in Banach spaces

    International Nuclear Information System (INIS)

    Chang, Y.-K.; Anguraj, A.; Mallika Arjunan, M.

    2009-01-01

    In this work, we establish a sufficient condition for the controllability of the first-order impulsive neutral functional differential inclusions with infinite delay in Banach spaces. The results are obtained by using the Dhage's fixed point theorem.

  4. Banach C*-algebras not containing a subspace isomorphic to C0

    International Nuclear Information System (INIS)

    Basit, B.

    1989-09-01

    If X is a locally Hausdorff space and C 0 (X) the Banach algebra of continuous functions defined on X vanishing at infinity, we showed that a subalgebra A of C 0 (X) is finite dimensional if it does not contain a subspace isomorphic to the Banach space C 0 of convergent to zero complex sequences. In this paper we extend this result to noncommutative Banach C*-algebras and Banach* algebras. 10 refs

  5. Fixed Points of α-Admissible Mappings in Cone Metric Spaces with Banach Algebra

    Directory of Open Access Journals (Sweden)

    S.K. Malhotra

    2015-11-01

    Full Text Available In this paper, we introduce the $\\alpha$-admissible mappings in the setting of cone metric spaces equipped with Banach algebra and solid cones. Our results generalize and extend several known results of metric and cone metric spaces. An example is presented which illustrates and shows the significance of results proved herein.

  6. Controllability of impulsive neutral functional differential inclusions with infinite delay in Banach spaces

    Energy Technology Data Exchange (ETDEWEB)

    Chang, Y.-K. [Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070 (China)], E-mail: lzchangyk@163.com; Anguraj, A. [Department of Mathematics, PSG College of Arts and Science, Coimbatore 641 014, Tamil Nadu (India)], E-mail: angurajpsg@yahoo.com; Mallika Arjunan, M. [Department of Mathematics, PSG College of Arts and Science, Coimbatore 641 014, Tamil Nadu (India)], E-mail: arjunphd07@yahoo.co.in

    2009-02-28

    In this work, we establish a sufficient condition for the controllability of the first-order impulsive neutral functional differential inclusions with infinite delay in Banach spaces. The results are obtained by using the Dhage's fixed point theorem.

  7. POSITIVE SOLUTIONS TO SEMI-LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACE

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.

  8. Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces

    Directory of Open Access Journals (Sweden)

    Si-Huan Li

    2013-01-01

    Full Text Available The concept of sharp efficient solution for vector equilibrium problems on Banach spaces is proposed. Moreover, the Fermat rules for local efficient solutions of vector equilibrium problems are extended to the sharp efficient solutions by means of the Clarke generalized differentiation and the normal cone. As applications, some necessary optimality conditions and sufficient optimality conditions for local sharp efficient solutions of a vector optimization problem with an abstract constraint and a vector variational inequality are obtained, respectively.

  9. The Ascoli property for function spaces and the weak topology of Banach and Fréchet spaces

    Czech Academy of Sciences Publication Activity Database

    Gabriyelyan, S.; Kąkol, Jerzy; Plebanek, G.

    2016-01-01

    Roč. 233, č. 2 (2016), s. 119-139 ISSN 0039-3223 R&D Projects: GA ČR GF16-34860L Institutional support: RVO:67985840 Keywords : locally convex-space Subject RIV: BA - General Mathematics Impact factor: 0.535, year: 2016 https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/233/2/91577/the-ascoli-property-for-function-spaces- and -the-weak-topology-of-banach- and -frechet-spaces

  10. The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces

    Directory of Open Access Journals (Sweden)

    Rabian Wangkeeree

    2012-01-01

    Full Text Available We introduce the general iterative methods for finding a common fixed point of asymptotically nonexpansive semigroups which is a unique solution of some variational inequalities. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature.

  11. Iterative solutions of nonlinear equations in smooth Banach spaces

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1994-05-01

    Let E be a smooth Banach space over the real field, φ not= K is contained in E closed convex and bounded, T:K → K uniformly continuous and strongly pseudo-contractive. It is proved that the Ishikawa iteration process converges strongly to the unique fixed point of T. Applications of this result to the operator equations Au=f or u+Au=f where A is a strongly accretive mapping of E into itself and under various continuity assumptions on A are also given. (author). 41 refs

  12. Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces

    Czech Academy of Sciences Publication Activity Database

    Caetano, A.M.; Gogatishvili, Amiran; Opic, B.

    2016-01-01

    Roč. 146, č. 5 (2016), s. 905-927 ISSN 0308-2105 R&D Projects: GA ČR GA13-14743S Institutional support: RVO:67985840 Keywords : quasi-Banach function space * compactness * compact embedding Subject RIV: BA - General Mathematics Impact factor: 1.158, year: 2016 http:// journals .cambridge.org/action/displayAbstract?fromPage=online&aid=10379393&fileId=S0308210515000761

  13. Some fixed point theorems in fuzzy reflexive Banach spaces

    International Nuclear Information System (INIS)

    Sadeqi, I.; Solaty kia, F.

    2009-01-01

    In this paper, we first show that there are some gaps in the fixed point theorems for fuzzy non-expansive mappings which are proved by Bag and Samanta, in [Bag T, Samanta SK. Fixed point theorems on fuzzy normed linear spaces. Inf Sci 2006;176:2910-31; Bag T, Samanta SK. Some fixed point theorems in fuzzy normed linear spaces. Inform Sci 2007;177(3):3271-89]. By introducing the notion of fuzzy and α- fuzzy reflexive Banach spaces, we obtain some results which help us to establish the correct version of fuzzy fixed point theorems. Second, by applying Theorem 3.3 of Sadeqi and Solati kia [Sadeqi I, Solati kia F. Fuzzy normed linear space and it's topological structure. Chaos, Solitons and Fractals, in press] which says that any fuzzy normed linear space is also a topological vector space, we show that all topological version of fixed point theorems do hold in fuzzy normed linear spaces.

  14. Linear embeddings of finite-dimensional subsets of Banach spaces into Euclidean spaces

    International Nuclear Information System (INIS)

    Robinson, James C

    2009-01-01

    This paper treats the embedding of finite-dimensional subsets of a Banach space B into finite-dimensional Euclidean spaces. When the Hausdorff dimension of X − X is finite, d H (X − X) k are injective on X. The proof motivates the definition of the 'dual thickness exponent', which is the key to proving that a prevalent set of such linear maps have Hölder continuous inverse when the box-counting dimension of X is finite and k > 2d B (X). A related argument shows that if the Assouad dimension of X − X is finite and k > d A (X − X), a prevalent set of such maps are bi-Lipschitz with logarithmic corrections. This provides a new result for compact homogeneous metric spaces via the Kuratowksi embedding of (X, d) into L ∞ (X)

  15. On a nonlinear integrodifferential evolution inclusion with nonlocal initial conditions in Banach spaces

    Directory of Open Access Journals (Sweden)

    Zuomao Yan

    2012-01-01

    Full Text Available In this paper, we discuss the existence results for a class of nnlinear integrodifferential evolution inclusions with nonlocal initial conditions in Banach spaces. Our results are based on a fixed point theorem for condensing maps due to Martelli and the resolvent operators combined with approximation techniques.

  16. Categories of dicompact BI- T 2 texture spaces and a Banach-stone ...

    African Journals Online (AJOL)

    The principal aim of this paper is to consider various aspects of the theory of dicompact bi-T2 texture spaces, and place them in a categorical setting. It culminates in a version of the Banach-Stone theorem. On the way, a new class of textures, called here nearly plain textures, is seen to play a crucial role in the development ...

  17. Multiple positive solutions for second order impulsive boundary value problems in Banach spaces

    Directory of Open Access Journals (Sweden)

    Zhi-Wei Lv

    2010-06-01

    Full Text Available By means of the fixed point index theory of strict set contraction operators, we establish new existence theorems on multiple positive solutions to a boundary value problem for second-order impulsive integro-differential equations with integral boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result.

  18. of Banach modules

    Directory of Open Access Journals (Sweden)

    Anousheh Fatemeh

    2015-10-01

    Full Text Available Let A be a Banach algebra, E be a Banach A-bimodule and Δ E → A be a bounded Banach A-bimodule homomorphism. It is shown that under some mild conditions, the weakΔ''-amenability of E'' (as an A''-bimodule necessitates weak Δ-amenability of E (as an A-bimodule. Some examples of weak-amenable Banach modules are provided as well.

  19. Strong Convergence Theorems of a New General Iterative Process with Meir-Keeler Contractions for a Countable Family of -Strict Pseudocontractions in -Uniformly Smooth Banach Spaces

    Directory of Open Access Journals (Sweden)

    Song Yanlai

    2010-01-01

    Full Text Available We introduce a new iterative scheme with Meir-Keeler contractions for strict pseudocontractions in -uniformly smooth Banach spaces. We also discuss the strong convergence theorems for the new iterative scheme in -uniformly smooth Banach space. Our results improve and extend the corresponding results announced by many others.

  20. On Landweber–Kaczmarz methods for regularizing systems of ill-posed equations in Banach spaces

    International Nuclear Information System (INIS)

    Leitão, A; Alves, M Marques

    2012-01-01

    In this paper, iterative regularization methods of Landweber–Kaczmarz type are considered for solving systems of ill-posed equations modeled (finitely many) by operators acting between Banach spaces. Using assumptions of uniform convexity and smoothness on the parameter space, we are able to prove a monotony result for the proposed method, as well as to establish convergence (for exact data) and stability results (in the noisy data case). (paper)

  1. An inner product for a Banach-algebra

    International Nuclear Information System (INIS)

    Mohammad, N.; Verjovsky, A.

    1988-07-01

    An inner product is defined on a commutative Banach algebra with an essential involution and the resultant inner product space is shown to be a topological algebra. Several conditions for its completeness are established and moreover, a decomposition theorem is proved. It is shown that every commutative Banach algebra with an essential involution has an auxiliary norm which turns it into an A*-algebra. (author). 6 refs

  2. Stochastic integration in Banach spaces theory and applications

    CERN Document Server

    Mandrekar, Vidyadhar

    2015-01-01

    Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integrati...

  3. On 2-Banach algebras

    International Nuclear Information System (INIS)

    Mohammad, N.; Siddiqui, A.H.

    1987-11-01

    The notion of a 2-Banach algebra is introduced and its structure is studied. After a short discussion of some fundamental properties of bivectors and tensor product, several classical results of Banach algebras are extended to the 2-Banach algebra case. A condition under which a 2-Banach algebra becomes a Banach algebra is obtained and the relation between algebra of bivectors and 2-normed algebra is discussed. 11 refs

  4. Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces

    Directory of Open Access Journals (Sweden)

    Yongjin Li

    2013-08-01

    Full Text Available We prove the Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces. That is, if y is an approximate solution of the differential equation $y''+ alpha y'(t +eta y = 0$ or $y''+ alpha y'(t +eta y = f(t$, then there exists an exact solution of the differential equation near to y.

  5. C0-semigroups of linear operators on some ultrametric Banach spaces

    Directory of Open Access Journals (Sweden)

    Toka Diagana

    2006-01-01

    Full Text Available C0-semigroups of linear operators play a crucial role in the solvability of evolution equations in the classical context. This paper is concerned with a brief conceptualization of C0-semigroups on (ultrametric free Banach spaces E. In contrast with the classical setting, the parameter of a given C0-semigroup belongs to a clopen ball Ωr of the ground field K. As an illustration, we will discuss the solvability of some homogeneous p-adic differential equations.

  6. A Mean Value Theorem for non Differentiable Mappings in Banach Spaces

    OpenAIRE

    Deville, Robert

    1995-01-01

    We prove that if f is a real valued lower semicontinuous function on a Banach space X and if there exists a C^1, real valued Lipschitz continuous function on X with bounded support and which is not identically equal to zero, then f is Lipschitz continuous of constant K provided all lower subgradients of f are bounded by K. As an application, we give a regularity result of viscosity supersolutions (or subsolutions) of Hamilton-Jacobi equations in infinite dimensions which sat...

  7. Remark on application of the Banach metric method to cosmology

    International Nuclear Information System (INIS)

    Szydlowski, M.; Heller, M.

    1982-01-01

    If the cosmological equations can be reduced to the form of a dynamic system, the space of all their solutions is a Banach space. The influence of different parameters on the dynamics of the world models can be easily studied by means of the Banach metric. The method is tested for the Friedman cosmological models perturbed by the bulk viscosity. (author)

  8. Existence and convergence theorems for a class of multi-valued variational inclusions in Banach spaces

    International Nuclear Information System (INIS)

    Chidume, C.E.; Zegeye, H.; Kazmi, K.R.

    2002-07-01

    An existence theorem for a new class of multi-valued variational inclusion problems is established in smooth Banach spaces. Further, it is shown that a sequence of a Mann-type iteration algorithm is strongly convergent to the solutions in this class of variational inclusion problems. (author)

  9. Some s-numbers of an integral operator of Hardy type in Banach function spaces

    Czech Academy of Sciences Publication Activity Database

    Edmunds, D.; Gogatishvili, Amiran; Kopaliani, T.; Samashvili, N.

    2016-01-01

    Roč. 207, July (2016), s. 76-97 ISSN 0021-9045 R&D Projects: GA ČR GA13-14743S Institutional support: RVO:67985840 Keywords : Hardy type operators * Banach function spaces * s- numbers * compact linear operators Subject RIV: BA - General Mathematics Impact factor: 0.931, year: 2016 http://www.sciencedirect.com/science/article/pii/S0021904516000265

  10. Parameter choice in Banach space regularization under variational inequalities

    International Nuclear Information System (INIS)

    Hofmann, Bernd; Mathé, Peter

    2012-01-01

    The authors study parameter choice strategies for the Tikhonov regularization of nonlinear ill-posed problems in Banach spaces. The effectiveness of any parameter choice for obtaining convergence rates depends on the interplay of the solution smoothness and the nonlinearity structure, and it can be expressed concisely in terms of variational inequalities. Such inequalities are link conditions between the penalty term, the norm misfit and the corresponding error measure. The parameter choices under consideration include an a priori choice, the discrepancy principle as well as the Lepskii principle. For the convenience of the reader, the authors review in an appendix a few instances where the validity of a variational inequality can be established. (paper)

  11. Fixed point iterations for strictly hemi-contractive maps in uniformly smooth Banach spaces

    International Nuclear Information System (INIS)

    Chidume, C.E.; Osilike, M.O.

    1993-05-01

    It is proved that the Mann iteration process converges strongly to the fixed point of a strictly hemi-contractive map in real uniformly smooth Banach spaces. The class of strictly hemi-contractive maps includes all strictly pseudo-contractive maps with nonempty fixed point sets. A related result deals with the Ishikawa iteration scheme when the mapping is Lipschitzian and strictly hemi-contractive. Our theorems generalize important known results. (author). 29 refs

  12. Separable Reduction and Supporting Properties of Fréchet-Like Normals in Banach Spaces

    Czech Academy of Sciences Publication Activity Database

    Fabian, Marián; Mordukhovich, B. S.

    1999-01-01

    Roč. 51, č. 1 (1999), s. 26-48 ISSN 0008-414X R&D Projects: GA AV ČR IAA1019702; GA ČR GA201/98/1449 Institutional research plan: CEZ:AV0Z1019905; CEZ:AV0Z1019905 Keywords : nonsmooth analysis * Banach spaces * separable reduction Subject RIV: BA - General Mathematics Impact factor: 0.357, year: 1999

  13. Stability analysis of solutions to nonlinear stiff Volterra functional differential equations in Banach spaces

    Institute of Scientific and Technical Information of China (English)

    LI Shoufu

    2005-01-01

    A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.

  14. A General Iterative Method for a Nonexpansive Semigroup in Banach Spaces with Gauge Functions

    Directory of Open Access Journals (Sweden)

    Kamonrat Nammanee

    2012-01-01

    Full Text Available We study strong convergence of the sequence generated by implicit and explicit general iterative methods for a one-parameter nonexpansive semigroup in a reflexive Banach space which admits the duality mapping Jφ, where φ is a gauge function on [0,∞. Our results improve and extend those announced by G. Marino and H.-K. Xu (2006 and many authors.

  15. Convergence rates and finite-dimensional approximations for nonlinear ill-posed problems involving monotone operators in Banach spaces

    International Nuclear Information System (INIS)

    Nguyen Buong.

    1992-11-01

    The purpose of this paper is to investigate convergence rates for an operator version of Tikhonov regularization constructed by dual mapping for nonlinear ill-posed problems involving monotone operators in real reflective Banach spaces. The obtained results are considered in combination with finite-dimensional approximations for the space. An example is considered for illustration. (author). 15 refs

  16. Simultaneous power factorization in modules over Banach algebras

    NARCIS (Netherlands)

    Jeu, de M.F.E.; Jiang, X.

    2017-01-01

    Let A be a Banach algebra with a bounded left approximate identity {eλ}λ∈Λ" role="presentation">{eλ}λ∈Λ, let π" role="presentation">π be a continuous representation of A on a Banach space X, and let S be a non-empty subset of X such that limλπ(eλ)s=s" role="presentation">limλπ(eλ)s=s uniformly on S.

  17. Stefan Banach

    Indian Academy of Sciences (India)

    Stefan Banach was judged to have poor eyesight and hence unfit to serve in the military; there- ... Although often attributed to Banach, this problem is not due to him. ... to Lwów in 1944 and assisted in the attempts to rebuild the university.

  18. On countable tightness and the Lindelöf property in non-archimedean Banach spaces

    Czech Academy of Sciences Publication Activity Database

    Kąkol, Jerzy; Kubzdela, A.; Perez-Garcia, C.

    2018-01-01

    Roč. 25, č. 1 (2018), s. 181-199 ISSN 0944-6532 R&D Projects: GA ČR GF16-34860L Institutional support: RVO:67985840 Keywords : non-archimedean Banach space s * weak topology * Lindelöf property Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.496, year: 2016 http://www.heldermann.de/JCA/JCA25/JCA251/jca25011.htm

  19. Contractivity and Exponential Stability of Solutions to Nonlinear Neutral Functional Differential Equations in Banach Spaces

    Institute of Scientific and Technical Information of China (English)

    Wan-sheng WANG; Shou-fu LI; Run-sheng YANG

    2012-01-01

    A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.

  20. On the unbounded behaviour for some non-autonomous systems in Banach spaces

    International Nuclear Information System (INIS)

    Djafari Rouhani, B.

    1991-09-01

    By modifying our previous methods and by using the notion of integral solution introduced by Benilan, we study the asymptotic behaviour of unbounded trajectories for the quasi-autonomous dissipative system: du/dt + Au is not an element of f where X is a real Banach space, A an accretive (possibly multivalued) operator in X x X, and f - f ∞ is an element of L p ((0, +∞);X) for some f ∞ is an element of X and 1 ≤ p < ∞. (author). 24 refs

  1. A survey of weighted substitution operators and generalizations of Banach-stone theorem

    OpenAIRE

    R. K. Singh

    2005-01-01

    The classical Banach-Stone theorem characterizes linear surjective isometries between C(K)-spaces. The main aim of this paper is to present a survey of Banach-Stone-theorem-type results between some function spaces. The weighted substitution operators play an important role in characterization of isometries, disjointness preserving operators, and lattice homomorphisms. Some open problems are given for further investigation.

  2. Approximation of fixed points of Lipschitz pseudo-contractive mapping in Banach spaces

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1988-01-01

    Let K be a subset of a real Banach space X. A mapping T:K → X is called pseudo-contractive if the inequality ||x-y|| ≤ ||(1+r)(x-y)-r(Tx-Ty)|| holds for all x,y in K and r > 0. Fixed points of Lipschitz pseudo-contractive maps are approximated under appropriate conditions, by an iteration process of the type introduced by W.R. Mann. This gives an affirmative answer to the problem stated by T.L. Hicks and J.R. Rubicek (J. Math. Anal. Appl. 59 (1977) 504). (author). 28 refs

  3. Estimates for Solutions of Differential Equations in a Banach Space via Commutators

    Directory of Open Access Journals (Sweden)

    Gil’ Michael

    2018-02-01

    Full Text Available In a Banach space we consider the equation dx(t/dt = (A + B(t×(t (t ≥ 0, where A is a constant bounded operator, and B(t is a bounded variable operator.Norm estimates for the solutions of the considered equation are derived in terms of the commutator AB(t − B(tA. These estimates give us sharp stability conditions. Our results are new even in the finite dimensional case.We also discuss applications of the obtained results to a class of integro-differential equations.

  4. On the existence of solutions for Volterra integral inclusions in Banach spaces

    Directory of Open Access Journals (Sweden)

    Evgenios P. Avgerinos

    1993-01-01

    Full Text Available In this paper we examine a class of nonlinear integral inclusions defined in a separable Banach space. For this class of inclusions of Volterra type we establish two existence results, one for inclusions with a convex-valued orientor field and the other for inclusions with nonconvex-valued orientor field. We present conditions guaranteeing that the multivalued map that represents the right-hand side of the inclusion is α-condensing using for the proof of our results a known fixed point theorem for α-condensing maps.

  5. Spectral theory of linear operators and spectral systems in Banach algebras

    CERN Document Server

    Müller, Vladimir

    2003-01-01

    This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The monograph should appeal both to students who would like to learn about spectral theory and to experts in the field. It can also serve as a reference book. The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem. This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach alg...

  6. Restrictive metric regularity and generalized differential calculus in Banach spaces

    Directory of Open Access Journals (Sweden)

    Bingwu Wang

    2004-10-01

    Full Text Available We consider nonlinear mappings f:X→Y between Banach spaces and study the notion of restrictive metric regularity of f around some point x¯, that is, metric regularity of f from X into the metric space E=f(X. Some sufficient as well as necessary and sufficient conditions for restrictive metric regularity are obtained, which particularly include an extension of the classical Lyusternik-Graves theorem in the case when f is strictly differentiable at x¯ but its strict derivative ∇f(x¯ is not surjective. We develop applications of the results obtained and some other techniques in variational analysis to generalized differential calculus involving normal cones to nonsmooth and nonconvex sets, coderivatives of set-valued mappings, as well as first-order and second-order subdifferentials of extended real-valued functions.

  7. Global Dynamical Systems Involving Generalized -Projection Operators and Set-Valued Perturbation in Banach Spaces

    Directory of Open Access Journals (Sweden)

    Yun-zhi Zou

    2012-01-01

    Full Text Available A new class of generalized dynamical systems involving generalized f-projection operators is introduced and studied in Banach spaces. By using the fixed-point theorem due to Nadler, the equilibrium points set of this class of generalized global dynamical systems is proved to be nonempty and closed under some suitable conditions. Moreover, the solutions set of the systems with set-valued perturbation is showed to be continuous with respect to the initial value.

  8. Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces

    Directory of Open Access Journals (Sweden)

    Shenghua Wang

    2013-01-01

    Full Text Available We first introduce the concept of Bregman asymptotically quasinonexpansive mappings and prove that the fixed point set of this kind of mappings is closed and convex. Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of Bregman asymptotically quasinonexpansive mappings in reflexive Banach spaces and prove strong convergence theorems. Our results extend the recent ones of some others.

  9. Additive Functional Inequalities in Banach Modules

    Directory of Open Access Journals (Sweden)

    An JongSu

    2008-01-01

    Full Text Available Abstract We investigate the following functional inequality in Banach modules over a -algebra and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a -algebra in the spirit of the Th. M. Rassias stability approach. Moreover, these results are applied to investigate homomorphisms in complex Banach algebras and prove the generalized Hyers-Ulam stability of homomorphisms in complex Banach algebras.

  10. Spatiality of Derivations of Operator Algebras in Banach Spaces

    Directory of Open Access Journals (Sweden)

    Quanyuan Chen

    2011-01-01

    Full Text Available Suppose that A is a transitive subalgebra of B(X and its norm closure A¯ contains a nonzero minimal left ideal I. It is shown that if δ is a bounded reflexive transitive derivation from A into B(X, then δ is spatial and implemented uniquely; that is, there exists T∈B(X such that δ(A=TA−AT for each A∈A, and the implementation T of δ is unique only up to an additive constant. This extends a result of E. Kissin that “if A¯ contains the ideal C(H of all compact operators in B(H, then a bounded reflexive transitive derivation from A into B(H is spatial and implemented uniquely.” in an algebraic direction and provides an alternative proof of it. It is also shown that a bounded reflexive transitive derivation from A into B(X is spatial and implemented uniquely, if X is a reflexive Banach space and A¯ contains a nonzero minimal right ideal I.

  11. Asymptotic aspect of derivations in Banach algebras

    Directory of Open Access Journals (Sweden)

    Jaiok Roh

    2017-02-01

    Full Text Available Abstract We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.

  12. Asymptotically Almost Periodic Solutions of Evolution Equations in Banach Spaces

    Science.gov (United States)

    Ruess, W. M.; Phong, V. Q.

    Tile linear abstract evolution equation (∗) u'( t) = Au( t) + ƒ( t), t ∈ R, is considered, where A: D( A) ⊂ E → E is the generator of a strongly continuous semigroup of operators in the Banach space E. Starting from analogs of Kadets' and Loomis' Theorems for vector valued almost periodic Functions, we show that if σ( A) ∩ iR is countable and ƒ: R → E is [asymptotically] almost periodic, then every bounded and uniformly continuous solution u to (∗) is [asymptotically] almost periodic, provided e-λ tu( t) has uniformly convergent means for all λ ∈ σ( A) ∩ iR. Related results on Eberlein-weakly asymptotically almost periodic, periodic, asymptotically periodic and C 0-solutions of (∗), as well as on the discrete case of solutions of difference equations are included.

  13. Generalized module extension Banach algebras: Derivations and ...

    African Journals Online (AJOL)

    Let A and X be Banach algebras and let X be an algebraic Banach A-module. Then the ℓ-1direct sum A x X equipped with the multiplication (a; x)(b; y) = (ab; ay + xb + xy) (a; b ∈ A; x; y ∈ X) is a Banach algebra, denoted by A ⋈ X, which will be called "a generalized module extension Banach algebra". Module extension ...

  14. Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in -Uniformly Smooth and Strictly Convex Banach Spaces

    Directory of Open Access Journals (Sweden)

    Meng Wen

    2012-01-01

    Full Text Available We introduce a new iterative scheme with Meir-Keeler contractions for an asymptotically nonexpansive mapping in -uniformly smooth and strictly convex Banach spaces. We also proved the strong convergence theorems of implicit and explicit schemes. The results obtained in this paper extend and improve many recent ones announced by many others.

  15. Relations between generalized von Neumann-Jordan and James constants for quasi-Banach spaces

    Directory of Open Access Journals (Sweden)

    Young Chel Kwun

    2016-07-01

    Full Text Available Abstract Let C N J ( B $\\mathcal{C}_{NJ} ( \\mathcal{B} $ and J ( B $J ( \\mathcal{B} $ be the generalized von Neumann-Jordan and James constants of a quasi-Banach space B $\\mathcal{B}$ , respectively. In this paper we shall show the relation between C N J ( B $\\mathcal {C}_{NJ} ( \\mathcal{B} $ , J ( B $J ( \\mathcal{B} $ , and the modulus of convexity. Also, we show that if B $\\mathcal{B}$ is not uniform non-square then J ( B = C N J ( B = 2 $J ( \\mathcal{B} =\\mathcal{C}_{NJ} ( \\mathcal{B} =2$ . Moreover, we give an equivalent formula for the generalized von Neumann-Jordan constant.

  16. Convergence theorems for a class of nonlinear maps in uniformly smooth Banach spaces

    International Nuclear Information System (INIS)

    Chidume, C.E.; Osilike, M.O.

    1992-05-01

    Let K be a nonempty closed and convex subset of a real uniformly smooth Banach space, E, with modulus of smoothness of power type q>1. Let T be a mapping of K into itself, T is an element of C (in the notion of Browder and Petryshyn; and Rhoades). It is proved that the Mann iteration process, under suitable conditions, converges strongly to the unique fixed point of T. If K is also bounded, then the Ishikawa iteration process converges to the fixed point of T. While our theorems generalize important known results, our method is also of independent interest. (author). 14 refs

  17. On character amenability of Banach algebras

    Science.gov (United States)

    Kaniuth, E.; Lau, A. T.; Pym, J.

    2008-08-01

    We continue our work [E. Kaniuth, A.T. Lau, J. Pym, On [phi]-amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc. 144 (2008) 85-96] in the study of amenability of a Banach algebra A defined with respect to a character [phi] of A. Various necessary and sufficient conditions of a global and a pointwise nature are found for a Banach algebra to possess a [phi]-mean of norm 1. We also completely determine the size of the set of [phi]-means for a separable weakly sequentially complete Banach algebra A with no [phi]-mean in A itself. A number of illustrative examples are discussed.

  18. Nonlinear Stability of ρ-Functional Equations in Latticetic Random Banach Lattice Spaces

    Directory of Open Access Journals (Sweden)

    Mohammad Maleki V.

    2018-02-01

    Full Text Available In this paper, we prove the generalized nonlinear stability of the first and second of the following ρ -functional equations, G ( | a | Δ A * | b | Δ B * G ( | a | Δ A * * | b | − G ( | a | Δ B * * G ( | b | = ρ ( 2 G | a | Δ A * | b | 2 Δ B * G | a | Δ A * * | b | 2 − G ( | a | Δ B * * G ( | b | , and 2 G | a | Δ A * | b | 2 Δ B * G | a | Δ A * * | b | 2 − G ( | a | Δ B * * G ( | b | = ρ G ( | a | Δ A * | b | Δ B * G ( | a | Δ A * * | b | − G ( | a | Δ B * * G ( | b | in latticetic random Banach lattice spaces, where ρ is a fixed real or complex number with ρ ≠ 1 .

  19. On the regularity of mild solutions to complete higher order differential equations on Banach spaces

    Directory of Open Access Journals (Sweden)

    Nezam Iraniparast

    2015-09-01

    Full Text Available For the complete higher order differential equation u(n(t=Σk=0n-1Aku(k(t+f(t, t∈ R (* on a Banach space E, we give a new definition of mild solutions of (*. We then characterize the regular admissibility of a translation invariant subspace al M of BUC(R, E with respect to (* in terms of solvability of the operator equation Σj=0n-1AjXal Dj-Xal Dn = C. As application, almost periodicity of mild solutions of (* is proved.

  20. Differential Equation over Banach Algebra

    OpenAIRE

    Kleyn, Aleks

    2018-01-01

    In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.

  1. Picard iterations for nonlinear Lipschitz strong pseudo-contractions in uniformly smooth Banach spaces

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1995-06-01

    Suppose E is a real uniformly smooth Banach space and K is a nonempty closed convex and bounded subset of E, T:K → K is a Lipschitz pseudo-contraction. It is proved that the Picard iterates of a suitably defined operator converges strongly to the unique fixed point of T. Furthermore, this result also holds for the slightly larger class of Lipschitz strong hemi-contractions. Related results deal with strong convergence of the Picard iterates to the unique solution of operator equations involving Lipschitz strongly accretive maps. Apart from establishing strong convergence, our theorems give existence, uniqueness and convergence-rate which is at least as fast as a geometric progression. (author). 51 refs

  2. Fredholm theory in ordered Banach algebras | Benjamin ...

    African Journals Online (AJOL)

    This paper illustrates some initial steps taken in the effort of unifying the theory of positivity in ordered Banach algebas (OBAs) with the general Fred-holm theory in Banach algebras. We introduce here upper Weyl and upper Browder elements in an OBA relative to an arbitrary Banach algebra homomorphism and investigate ...

  3. Several complex variables and Banach algebras

    International Nuclear Information System (INIS)

    Allan, G.R.

    1976-01-01

    This paper aims to present certain applications of the theory of holomorphic functions of several complex variables to the study of commutative Banach algebras. The material falls into the following sections: (A) Introcution to Banach algebras (this will not presuppose any knowledge of the subject); (B) Groups of differential forms (mainly concerned with setting up a useful language); (C) Polynomially convex domains. (D) Holomorphic functional calculus for Banach algebras; (E) Some applications of the functional calculus. (author)

  4. A System of Generalized Variational Inclusions Involving a New Monotone Mapping in Banach Spaces

    Directory of Open Access Journals (Sweden)

    Jinlin Guan

    2013-01-01

    Full Text Available We introduce a new monotone mapping in Banach spaces, which is an extension of the -monotone mapping studied by Nazemi (2012, and we generalize the variational inclusion involving the -monotone mapping. Based on the new monotone mapping, we propose a new proximal mapping which combines the proximal mapping studied by Nazemi (2012 with the mapping studied by Lan et al. (2011 and show its Lipschitz continuity. Based on the new proximal mapping, we give an iterative algorithm. Furthermore, we prove the convergence of iterative sequences generated by the algorithm under some appropriate conditions. Our results improve and extend corresponding ones announced by many others.

  5. Banach Synaptic Algebras

    Science.gov (United States)

    Foulis, David J.; Pulmannov, Sylvia

    2018-04-01

    Using a representation theorem of Erik Alfsen, Frederic Schultz, and Erling Størmer for special JB-algebras, we prove that a synaptic algebra is norm complete (i.e., Banach) if and only if it is isomorphic to the self-adjoint part of a Rickart C∗-algebra. Also, we give conditions on a Banach synaptic algebra that are equivalent to the condition that it is isomorphic to the self-adjoint part of an AW∗-algebra. Moreover, we study some relationships between synaptic algebras and so-called generalized Hermitian algebras.

  6. Weak Convergence and Banach Space-Valued Functions: Improving the Stability Theory of Feynman’s Operational Calculi

    International Nuclear Information System (INIS)

    Nielsen, Lance

    2011-01-01

    In this paper we investigate the relation between weak convergence of a sequence {μ n } of probability measures on a Polish space S converging weakly to the probability measure μ and continuous, norm-bounded functions into a Banach space X. We show that, given a norm-bounded continuous function f:S→X, it follows that lim n∞ ∫ S f, dμ n = ∫ S f, dμ —the limit one has for bounded and continuous real (or complex)—valued functions on S. This result is then applied to the stability theory of Feynman’s operational calculus where it is shown that the theory can be significantly improved over previous results.

  7. Moduli and Characteristics of Monotonicity in Some Banach Lattices

    Directory of Open Access Journals (Sweden)

    Miroslav Krbec

    2010-01-01

    Full Text Available First the characteristic of monotonicity of any Banach lattice X is expressed in terms of the left limit of the modulus of monotonicity of X at the point 1. It is also shown that for Köthe spaces the classical characteristic of monotonicity is the same as the characteristic of monotonicity corresponding to another modulus of monotonicity δ^m,E. The characteristic of monotonicity of Orlicz function spaces and Orlicz sequence spaces equipped with the Luxemburg norm are calculated. In the first case the characteristic is expressed in terms of the generating Orlicz function only, but in the sequence case the formula is not so direct. Three examples show why in the sequence case so direct formula is rather impossible. Some other auxiliary and complemented results are also presented. By the results of Betiuk-Pilarska and Prus (2008 which establish that Banach lattices X with ε0,m(X<1 and weak orthogonality property have the weak fixed point property, our results are related to the fixed point theory (Kirk and Sims (2001.

  8. Logarithmic residues in Banach algebras

    NARCIS (Netherlands)

    H. Bart (Harm); T. Ehrhardt; B. Silbermann

    1994-01-01

    textabstractLet f be an analytic Banach algebra valued function and suppose that the contour integral of the logarithmic derivative f′f-1 around a Cauchy domain D vanishes. Does it follow that f takes invertible values on all of D? For important classes of Banach algebras, the answer is positive. In

  9. Strong convergence theorems for uniformly L-Lipschitzian mappings in Banach spaces

    International Nuclear Information System (INIS)

    Chidume, C.E.; Ofoedu, E.U.

    2007-07-01

    Let E be a real reflexive Banach space with uniform Gateaux differentiable norm, K be a nonempty bounded closed and convex subset of E , T : K → K be a uniformly L-Lipschitzian mapping such that F (T) := {x element of K : Tx = x} ≠ 0, u element of K be fixed and let {α n } n≥0 and {γ n } n≥0 subset of (0, 1) be such that lim n→∞ α n = 0 = lim n→ ∞ γ n and lim n→ ∞(β n - 1)/ α n = 0, where β n Σ j=0 n λ j and λ j = 1 + α j γ j L. Let S n := (1 - α n γ n )I + α n γ n T n . It is proved that there exists some integer N 0 > 1, such that for each n ≥ N 0 , there exists unique x n element of K such that x n = α n u+(1 -α n ) 1/ (n + 1) Σ j=0 n S j x n . If φ : E → R is defined by φ (y) := LIM n vertical bar vertical bar x n -y vertical bar vertical bar 2 for all y element of E here LIM denotes a Banach limit, vertical bar vertical bar x n - Tx n vertical bar vertical bar → 0 as n → ∞ and K min intersection F (T) ≠ 0, where K min := {x element of E : φ (x) = min (u element of K) φ (u) }, then it is proved that {x n } converges strongly to a fixed point of T. As an application, it is proved that the iterative process, z 0 element of K, z n+1 alpha# n u + (1 - α n ) 1/ (n + 1) Σ j=0 n S j z n , n ≥ 0, under suitable conditions on the iteration parameters, converges strongly to a fixed point of T. (author)

  10. Module-Amenability on Module Extension Banach Algebras

    Directory of Open Access Journals (Sweden)

    Davood Ebrahimi Bagha

    2014-05-01

    Full Text Available Let $A$ be a Banach algebra and $E$ be a Banach‎ ‎$A$-bimodule then $S=A\\oplus E$‎, ‎the $l^1$-direct sum of $A$ and $E$‎ ‎becomes a module extension Banach algebra when equipped with the‎ ‎algebras product $ (a‎ , ‎x‎. ‎(a'‎, ‎x' = (aa'‎ , ‎a.x'‎ + ‎x.a'$‎. ‎In this‎ ‎paper‎, ‎we investigate $\\triangle$-amenability for these Banach‎ ‎algebras and we show that for discrete inverse semigroup $S$ with‎ ‎the set of idempotents $E_{S}$‎, ‎the module extension Banach algebra $S=l^{1} (E_{S} \\op l^{1} (S$ is $ \\tr$-amenable‎ ‎as a $l^{1}(E_{S} $-module if and only if $l^{1}(E_{S}$ is amenable as Banach algebra‎.

  11. Application of Pettis integration to differential inclusions with three-point boundary conditions in Banach spaces

    Directory of Open Access Journals (Sweden)

    Imen Boutana

    2007-12-01

    Full Text Available This paper provide some applications of Pettis integration to differential inclusions in Banach spaces with three point boundary conditions of the form $$ ddot{u}(t in F(t,u(t,dot u(t+H(t,u(t,dot u(t,quad hbox{a.e. } t in [0,1], $$ where $F$ is a convex valued multifunction upper semicontinuous on $Eimes E$ and $H$ is a lower semicontinuous multifunction. The existence of solutions is obtained under the non convexity condition for the multifunction $H$, and the assumption that $F(t,x,ysubset Gamma_{1}(t$, $H(t,x,ysubset Gamma_{2}(t$, where the multifunctions $Gamma_{1},Gamma_{2}:[0,1] ightrightarrows E$ are uniformly Pettis integrable.

  12. Banach Gelfand Triples for Applications in Physics and Engineering

    Science.gov (United States)

    Feichtinger, Hans G.

    2009-07-01

    The principle of extension is widespread within mathematics. Starting from simple objects one constructs more sophisticated ones, with a kind of natural embedding from the set of old objects to the new, enlarged set. Usually a set of operations on the old set can still be carried out, but maybe also some new ones. Done properly one obtains more completed objects of a similar kind, with additional useful properties. Let us give a simple example: While multiplication and addition can be done exactly and perfectly in the setting of Q, the rational numbers, the field R of real numbers has the advantage of being complete (Cauchy sequences have a limit…) and hence allowing for numbers like π or √2 . Finally the even "more complicated" field C of complex numbers allows to find solutions to equations like z2 = -1. The chain of inclusions of fields, Q⊂R⊂C is a good motivating example in the domain of "numbers." The main subject of the present survey-type article is a new theory of Banach Gelfand triples (BGTs), providing a similar setting in the context of (generalized) functions. Test functions are the simple objects, elements of the Hilbert space L2(Rd) are well suited in order to describe concepts of orthogonality, and they can be approximated to any given precision (in the ‖ṡ‖2-norm) by test functions. Finally one needs an even larger (Banach) space of generalized functions resp. distributions, containing among others pure frequencies and Dirac measures in order to describe various mappings between such Banach Gelfand triples in terms of the most important "elementary building blocks," in a clear analogy to the finite/discrete setting (where Dirac measures correspond to unit vectors). Our concrete Banach Gelfand triple is based on the Segal algebra S0(Rd), which coincides with the modulation space M1(Rd) = M01,1(Rd), and plays a very important and natural role for time-frequency analysis. We will point out that it provides the appropriate setting for a

  13. An inner product for a Banach-algebra

    International Nuclear Information System (INIS)

    Noor, M.; Verjovsky, A.

    1987-10-01

    An intrinsic inner product for a commutative Banach*-algebra is defined. Several conditions for its completeness are established. It is shown that any Banach*-algebra with proper and continuous involution has an auxiliary norm that turns it into an A*-algebra. (author). 7 refs

  14. On the Cauchy Functional Inequality in Banach Modules

    Directory of Open Access Journals (Sweden)

    Park Choonkil

    2008-01-01

    Full Text Available Abstract We investigate the following functional inequality: in Banach modules over a -algebra, and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a -algebra.

  15. A note on the L-fuzzy Banach's contraction principle

    International Nuclear Information System (INIS)

    Martinez-Moreno, J.; Roldan, A.; Roldan, C.

    2009-01-01

    Recently, Alaca et al. [Alaca C, Turkoglu D, Yildiz C. Fixed points in intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2006;29:10738] proved fuzzy Banach fixed point theorem in intuitionistic fuzzy metric spaces and Saadati [Saadati R. Notes to the paper 'fixed points in intuitionistic fuzzy metric spaces' and its generalization to L-fuzzy metric spaces. Chaos, Solitions and Fractals 2008;35:80-176] extended it in generalized fuzzy metric spaces. The purpose of this paper is to give a correct proof of the main result in Saadati [Saadati R. Notes to the paper 'fixed points in intuitionistic fuzzy metric spaces' and its generalization to L-fuzzy metric spaces. Chaos, Solitions and Fractals 2008;35:80-176].

  16. Hereditary properties of Amenability modulo an ideal of Banach algebras

    Directory of Open Access Journals (Sweden)

    Hamidreza Rahimi

    2014-10-01

    Full Text Available In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show thatif $(e_{\\alpha}_{\\alpha}$ is a bounded approximate identity modulo $I$ of a Banach algebra $A$ and $X$ is a neo-unital modulo $I$, then $(e_{\\alpha}_{\\alpha}$ is a bounded approximate identity for $X$. Moreover we show that amenability modulo an ideal of a Banach algebra $A$ can be only considered by the neo-unital modulo $I$ Banach algebra over $A$

  17. Erratum to: “Polynomial algebras on classical Banach spaces”

    Czech Academy of Sciences Publication Activity Database

    D'Alessandro, Stefania; Hájek, Petr Pavel; Johanis, M.

    2015-01-01

    Roč. 207, č. 2 (2015), s. 1003-1012 ISSN 0021-2172 R&D Projects: GA ČR(CZ) GAP201/11/0345; GA MŠk(CZ) 7AMB12FR003 Institutional support: RVO:67985840 Keywords : Banach space * polynomial algebra Subject RIV: BA - General Mathematics Impact factor: 0.738, year: 2015 http://link.springer.com/article/10.1007%2Fs11856-015-1155-y

  18. Modern methods in topological vector spaces

    CERN Document Server

    Wilansky, Albert

    2013-01-01

    Designed for a one-year course in topological vector spaces, this text is geared toward advanced undergraduates and beginning graduate students of mathematics. The subjects involve properties employed by researchers in classical analysis, differential and integral equations, distributions, summability, and classical Banach and Frechét spaces. Optional problems with hints and references introduce non-locally convex spaces, Köthe-Toeplitz spaces, Banach algebra, sequentially barrelled spaces, and norming subspaces.Extensive introductory chapters cover metric ideas, Banach space, topological vect

  19. Asymptotic behaviour of solutions of nonlinear delay difference equations in Banach spaces

    Directory of Open Access Journals (Sweden)

    Anna Kisiolek

    2005-10-01

    Full Text Available We consider the second-order nonlinear difference equations of the form Δ(rn−1Δxn−1+pnf(xn−k=hn. We show that there exists a solution (xn, which possesses the asymptotic behaviour ‖xn−a∑j=0n−1(1/rj+b‖=o(1, a,b∈ℝ. In this paper, we extend the results of Agarwal (1992, Dawidowski et al. (2001, Drozdowicz and Popenda (1987, M. Migda (2001, and M. Migda and J. Migda (1988. We suppose that f has values in Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.

  20. Derivations into duals of ideals of Banach algebras

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    We say that Y is a dual A-bimodule if there is a Banach A-bimodule X such that Y is ... D is inner; this definition was introduced by Johnson [Jo1]. ..... [Pa] Palmer Theodore W, Banach algebra and the general theory of ∗-algebras (Cam-.

  1. Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces

    Directory of Open Access Journals (Sweden)

    P. Pasom

    2012-01-01

    Full Text Available Let C be a nonempty bounded closed convex subset of a complete CAT(0 space X. We prove that the common fixed point set of any commuting family of asymptotic pointwise nonexpansive mappings on C is nonempty closed and convex. We also show that, under some suitable conditions, the sequence {xk}k=1∞ defined by xk+1=(1-tmkxk⊕tmkTmnky(m-1k, y(m-1k=(1-t(m-1kxk⊕t(m-1kTm-1nky(m-2k,y(m-2k=(1-t(m-2kxk⊕t(m-2kTm-2nky(m-3k,…,y2k=(1-t2kxk⊕t2kT2nky1k,y1k=(1-t1kxk⊕t1kT1nky0k,y0k=xk,  k∈N, converges to a common fixed point of T1,T2,…,Tm where they are asymptotic pointwise nonexpansive mappings on C, {tik}k=1∞ are sequences in [0,1] for all i=1,2,…,m, and {nk} is an increasing sequence of natural numbers. The related results for uniformly convex Banach spaces are also included.

  2. Mixed gradient-Tikhonov methods for solving nonlinear ill-posed problems in Banach spaces

    International Nuclear Information System (INIS)

    Margotti, Fábio

    2016-01-01

    Tikhonov regularization is a very useful and widely used method for finding stable solutions of ill-posed problems. A good choice of the penalization functional as well as a careful selection of the topologies of the involved spaces is fundamental to the quality of the reconstructions. These choices can be combined with some a priori information about the solution in order to preserve desired characteristics like sparsity constraints for example. To prove convergence and stability properties of this method, one usually has to assume that a minimizer of the Tikhonov functional is known. In practical situations however, the exact computation of a minimizer is very difficult and even finding an approximation can be a very challenging and expensive task if the involved spaces have poor convexity or smoothness properties. In this paper we propose a method to attenuate this gap between theory and practice, applying a gradient-like method to a Tikhonov functional in order to approximate a minimizer. Using only available information, we explicitly calculate a maximal step-size which ensures a monotonically decreasing error. The resulting algorithm performs only finitely many steps and terminates using the discrepancy principle. In particular the knowledge of a minimizer or even its existence does not need to be assumed. Under standard assumptions, we prove convergence and stability results in relatively general Banach spaces, and subsequently, test its performance numerically, reconstructing conductivities with sparsely located inclusions and different kinds of noise in the 2D electrical impedance tomography. (paper)

  3. Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras

    Directory of Open Access Journals (Sweden)

    Madjid Eshaghi Gordji

    2012-01-01

    Full Text Available Let n>1 be an integer, let A be an algebra, and X be an A-module. A quadratic function D:A→X is called a quadratic n-derivation if D(∏i=1nai=D(a1a22⋯an2+a12D(a2a32⋯an2+⋯+a12a22⋯an−12D(an for all a1,...,an∈A. We investigate the Hyers-Ulam stability of quadratic n-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.

  4. The Banach-Tarski paradox

    CERN Document Server

    Wagon, Stan

    1985-01-01

    The Banach-Tarski paradox is a most striking mathematical construction: it asserts that a solid ball may be taken apart into finitely many pieces that can be rearranged using rigid motions to form a ball twice as large as the original. This volume explore

  5. (L) Sets and almost (L) seys in Banach lattices | Aqzzouz ...

    African Journals Online (AJOL)

    We characterize (L) sets and almost (L) sets in Banach lattices. Also, we look at Banach lattices in which these two classes of sets coincide. Keywords: (L) sets, Dunford-Pettis operator, almost Dunford-Pettis operator. Quaestiones Mathematicae 36(2013), 107-118 ...

  6. Alice and Bob meet Banach the interface of asymptotic geometric analysis and quantum information theory

    CERN Document Server

    Aubrun, Guillaume

    2017-01-01

    The quest to build a quantum computer is arguably one of the major scientific and technological challenges of the twenty-first century, and quantum information theory (QIT) provides the mathematical framework for that quest. Over the last dozen or so years, it has become clear that quantum information theory is closely linked to geometric functional analysis (Banach space theory, operator spaces, high-dimensional probability), a field also known as asymptotic geometric analysis (AGA). In a nutshell, asymptotic geometric analysis investigates quantitative properties of convex sets, or other geometric structures, and their approximate symmetries as the dimension becomes large. This makes it especially relevant to quantum theory, where systems consisting of just a few particles naturally lead to models whose dimension is in the thousands, or even in the billions. Alice and Bob Meet Banach is aimed at multiple audiences connected through their interest in the interface of QIT and AGA: at quantum information resea...

  7. A generalised Green-Julg theorem for proper groupoids and Banach algebras

    OpenAIRE

    Paravicini, Walther

    2009-01-01

    The Green-Julg theorem states that K_0^G(B) is isomorphic to K_0(L^1(G,B)) for every compact group G and every G-C*-algebra B. We formulate a generalisation of this result to proper groupoids and Banach algebras and deduce that the Bost assembly map is surjective for proper Banach algebras. On the way, we show that the spectral radius of an element in a C_0(X)-Banach algebra can be calculated from the spectral radius in the fibres.

  8. φ-Multipliers on Banach Algebras and Topological Modules

    OpenAIRE

    Adib, Marjan

    2015-01-01

    We prove some results concerning Arens regularity and amenability of the Banach algebra ${M}_{\\phi }(A)$ of all $\\phi $ -multipliers on a given Banach algebra $A$ . We also consider $\\phi $ -multipliers in the general topological module setting and investigate some of their properties. We discuss the $\\phi $ -strict and $\\phi $ -uniform topologies on ${M}_{\\phi }(A)$ . A characterization of $\\phi $ -multipliers on ${L}_{1}(G)$ -module ${L}_{p}(G)$ , where $G$ is a compact group, is given.

  9. Approximate cohomology in Banach algebras | Pourabbas ...

    African Journals Online (AJOL)

    We introduce the notions of approximate cohomology and approximate homotopy in Banach algebras and we study the relation between them. We show that the approximate homotopically equivalent cochain complexes give the same approximate cohomologies. As a special case, approximate Hochschild cohomology is ...

  10. On the L-characteristic of nonlinear superposition operators in lp-spaces

    International Nuclear Information System (INIS)

    Dedagic, F.

    1995-04-01

    In this paper we describe the L-characteristic of the nonlinear superposition operator F(x) f(s,x(s)) between two Banach spaces of functions x from N to R. It was shown that L-characteristic of the nonlinear superposition operator which acts between two Lebesgue spaces has so-called Σ-convexity property. In this paper we show that L-characteristic of the operator F (between two Banach spaces) has the convexity property. It means that the classical interpolation theorem of Reisz-Thorin for a linear operator holds for the nonlinear operator superposition which acts between two Banach spaces of sequences. Moreover, we consider the growth function of the operator superposition in mentioned spaces and we show that one has the logarithmically convexity property. (author). 7 refs

  11. Superstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (I

    Directory of Open Access Journals (Sweden)

    Rassias JM

    2009-01-01

    Full Text Available We discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module. Let be a Banach algebra and a Banach -module, and . The mappings , and are defined and it is proved that if (resp., is dominated by then is a generalized (resp., linear module- left derivation and is a (resp., linear module- left derivation. It is also shown that if (resp., is dominated by then is a generalized (resp., linear module- derivation and is a (resp., linear module- derivation.

  12. Vector measures on delta-rings and representation theorems of banach lattices

    OpenAIRE

    JUAN BLANCO, MARÍA ARÁNZAZU

    2011-01-01

    El espacio de funciones integrables con respecto a una medida vectorial, amén de interesante en si mismo, sirve de herramienta para aplicaciones en problemas importantes como la representación integral y el estudio del dominio óptimo de operadores lineales o la representación de retículos de Banach abstractos como espacios de funciones. Las medidas vectoriales clásicas se definen sobre -álgebras y con valores en un espacio de Banach, y los espacios correspondientes L1( ) y L1w( ) de funcio...

  13. Uniform Smoothness Entails Hahn-Banach | Albius | Quaestiones ...

    African Journals Online (AJOL)

    the Axiom of Choice), and we denote by ZFC set theory with the Axiom of Choice. Our paper deals with the role of the Axiom of. Choice in functional analysis, and more particularly, with the necessity of using the Axiom of Choice when invoking some consequence of the following Hahn-Banach axiom HB. Mathematics ...

  14. Schur spaces and weighted spaces of type H

    African Journals Online (AJOL)

    We extend some results related to composition operators on Hv(G) to arbitrary linear operators on Hv0 (G) and Hv(G). We also give examples of rank-one operators on Hv(G) which cannot be approximated by composition operators. Keywords: Weighted Banach spaces of holomorphic functions, Schur spaces, weakly ...

  15. When L1 of a vector measure is an AL-space

    OpenAIRE

    Curbera Costello, Guillermo

    1994-01-01

    We consider the space of real functions which are integrable with respect to a countably additive vector measure with values in a Banach space. In a previous paper we showed that this space can be any order continuous Banach lattice with weak order unit. We study a priori conditions on the vector measure in order to guarantee that the resulting L is order isomorphic to an AL-space. We prove that for separable measures with no atoms there exists a Co-valued measure that generates the same spac...

  16. Compact groups of positive operators on Banach lattices

    NARCIS (Netherlands)

    Jeu, de M.F.E.; Wortel, M.R.

    2014-01-01

    In this paper, we study groups of positive operators on Banach lattices. If a certain factorization property holds for the elements of such a group, the group has a homomorphic image in the isometric positive operators which has the same invariant ideals as the original group. If the group is

  17. Survey on nonlocal games and operator space theory

    Energy Technology Data Exchange (ETDEWEB)

    Palazuelos, Carlos, E-mail: cpalazue@mat.ucm.es [Instituto de Ciencias Matemáticas (ICMAT), Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid (Spain); Vidick, Thomas, E-mail: vidick@cms.caltech.edu [Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California 91125 (United States)

    2016-01-15

    This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.

  18. Survey on nonlocal games and operator space theory

    International Nuclear Information System (INIS)

    Palazuelos, Carlos; Vidick, Thomas

    2016-01-01

    This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states

  19. Another extension of Orlicz-Sobolev spaces to metric spaces

    Directory of Open Access Journals (Sweden)

    Noureddine Aïssaoui

    2004-01-01

    Full Text Available We propose another extension of Orlicz-Sobolev spaces to metric spaces based on the concepts of the Φ-modulus and Φ-capacity. The resulting space NΦ1 is a Banach space. The relationship between NΦ1 and MΦ1 (the first extension defined in Aïssaoui (2002 is studied. We also explore and compare different definitions of capacities and give a criterion under which NΦ1 is strictly smaller than the Orlicz space LΦ.

  20. 2-Local derivations on matrix algebras over semi-prime Banach algebras and on AW*-algebras

    International Nuclear Information System (INIS)

    Ayupov, Shavkat; Kudaybergenov, Karimbergen

    2016-01-01

    The paper is devoted to 2-local derivations on matrix algebras over unital semi-prime Banach algebras. For a unital semi-prime Banach algebra A with the inner derivation property we prove that any 2-local derivation on the algebra M 2 n (A), n ≥ 2, is a derivation. We apply this result to AW*-algebras and show that any 2-local derivation on an arbitrary AW*-algebra is a derivation. (paper)

  1. When is multiplication in a Banach algebra open?

    Czech Academy of Sciences Publication Activity Database

    Draga, Szymon; Kania, Tomasz

    2018-01-01

    Roč. 538, 1 February (2018), s. 149-165 ISSN 0024-3795 R&D Projects: GA ČR GF16-34860L Institutional support: RVO:67985840 Keywords : Banach algebra * open mapping * uniformly open map Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.973, year: 2016 http://www.sciencedirect.com/science/ article /pii/S0024379517305761?via%3Dihub

  2. On inessential elements in different Banach algebras | Behrendt ...

    African Journals Online (AJOL)

    If B is a subalgebra of a Banach algebra A we consider the problem of determining conditions that ensure that an element of B that exhibits a property in B also exhibits this property when viewed as an element of A. Further, we consider the converse problem whereby an element of B exhibiting a property in A also exhibits ...

  3. When is multiplication in a Banach algebra open?

    Czech Academy of Sciences Publication Activity Database

    Draga, Szymon; Kania, Tomasz

    2018-01-01

    Roč. 538, 1 February (2018), s. 149-165 ISSN 0024-3795 R&D Projects: GA ČR GF16-34860L Institutional support: RVO:67985840 Keywords : Banach algebra * open mapping * uniformly open map Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.973, year: 2016 http://www.sciencedirect.com/science/article/pii/S0024379517305761?via%3Dihub

  4. Characterization of associate spaces of weighted Lorentz spaces with applications

    Czech Academy of Sciences Publication Activity Database

    Gogatishvili, Amiran; Pick, L.; Soudský, F.

    2014-01-01

    Roč. 224, č. 1 (2014), s. 1-23 ISSN 0039-3223 R&D Projects: GA ČR GA13-14743S Institutional support: RVO:67985840 Keywords : weighted Lorentz spaces * weighted inequalities * non-increasing rearragement * Banach function space Subject RIV: BA - General Mathematics Impact factor: 0.610, year: 2014 http://journals.impan.gov.pl/sm/Inf/224-1-1.html

  5. Extremely strict ideals in Banach spaces

    Indian Academy of Sciences (India)

    Abstract. Motivated by the notion of an ideal introduced by Godefroy et al. (Stu- dia Math. 104 (1993) 13–59), in this article, we introduce and study the notion of an extremely strict ideal. For a Poulsen simplex K, we show that the space of affine contin- uous functions on K is an extremely strict ideal in the space of continuous ...

  6. On the paper: Numerical radius preserving linear maps on Banach algebras

    OpenAIRE

    El Azhari , Mohammed

    2017-01-01

    International audience; We give an example of a unital commutative complex Banach algebra having a normalized state which is not a spectral state and admitting an extreme normalized state which is not multiplicative. This disproves two results by Golfarshchi and Khalilzadeh.

  7. Star product realizations of kappa-Minkowski space

    DEFF Research Database (Denmark)

    Durhuus, Bergfinnur; Sitarz, Andrzej

    2013-01-01

    We define a family of star products and involutions associated with κ -Minkowski space. Applying corresponding quantization maps we show that these star products restricted to a certain space of Schwartz functions have isomorphic Banach algebra completions. For two particular star products...

  8. Unconditionally convergent series in the space C(Q)

    International Nuclear Information System (INIS)

    Basit, B.

    1981-08-01

    Let B be a Banach space and B* its dual Banach space. B contains csub(0) (B does not contain csub(0)) if B contains (does not contain) a subspace isomorphic to the space csub(0) of sequences of numbers tending to zero. The series Σsub(n=1)sup(infinity) xsub(n) of elements of B is weakly unconditionally convergent (w.u.c.) iff Σsub(n=1)sup(infinity)|x*(xsub(n))| 0 . Series of elements of C(Q) are considered here. Subspaces of C(Q) isomorphic to c 0 are constructed, and criteria for a series of elements of C(Q) to be w.u.c. or u.c. are given. Finally, an improved theorem of giving characterizations of the elements of subalgebras of C(Q) not containing c 0 is presented

  9. Integración en espacios de Banach

    OpenAIRE

    Rodríguez Ruiz, José

    2006-01-01

    Esta tesis doctoral se enmarca dentro de la teoría de integración de funciones con valores en espacios de Banach. Analizamos con detalle la integral de Birkhoff de funciones vectoriales, así como sus correspondientes versiones dentro de los contextos de la integración respecto de medidas vectoriales y la integración de multi-funciones. Comparamos estos métodos de integración con otros bien conocidos (integrales de Bochner, Pettis, McShane, Debreu, etc.). Caracterizamos, en términos de integra...

  10. Sobre la diferenciabilidad de funciones en espacios de Banach

    Directory of Open Access Journals (Sweden)

    Roberto C. Cabrales

    2006-01-01

    Full Text Available Se da un criterio que establece la diferenciabilidad de una función f : X → Y , donde X y Y son espacios de Banach. Este criterio se aplica además para obtener las reglas usuales del cálculo diferencial de una forma elemental, y también para obtener la diferenciabilidad de algunas normas de espacios funcionales clásicos.

  11. Superstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (I

    Directory of Open Access Journals (Sweden)

    Huai-Xin Cao

    2009-01-01

    Full Text Available We discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module. Let 𝒜 be a Banach algebra and X a Banach 𝒜-module, f:X→X and g:𝒜→𝒜. The mappings Δf,g1, Δf,g2, Δf,g3, and Δf,g4 are defined and it is proved that if ∥Δf,g1(x,y,z,w∥ (resp., ∥Δf,g3(x,y,z,w,α,β∥ is dominated by φ(x,y,z,w, then f is a generalized (resp., linear module-𝒜 left derivation and g is a (resp., linear module-X left derivation. It is also shown that if ∥Δf,g2(x,y,z,w∥ (resp., ∥Δf,g4(x,y,z,w,α,β∥ is dominated by φ(x,y,z,w, then f is a generalized (resp., linear module-𝒜 derivation and g is a (resp., linear module-X derivation.

  12. Central limit theorem for the Banach-valued weakly dependent random variables

    International Nuclear Information System (INIS)

    Dmitrovskij, V.A.; Ermakov, S.V.; Ostrovskij, E.I.

    1983-01-01

    The central limit theorem (CLT) for the Banach-valued weakly dependent random variables is proved. In proving CLT convergence of finite-measured (i.e. cylindrical) distributions is established. A weak compactness of the family of measures generated by a certain sequence is confirmed. The continuity of the limiting field is checked

  13. Quasi-Banach spaces of almost universal disposition

    Czech Academy of Sciences Publication Activity Database

    Sánchez, C. F.; Garbulińska, J.; Kubiś, Wieslaw

    2014-01-01

    Roč. 267, č. 3 (2014), s. 744-771 ISSN 0022-1236 R&D Projects: GA ČR(CZ) GAP201/12/0290 Institutional support: RVO:67985840 Keywords : p-Gurarii space * space of universal disposition * isometry Subject RIV: BA - General Mathematics Impact factor: 1.322, year: 2014 http://www.sciencedirect.com/science/article/pii/S0022123614002043

  14. ??ndice num??rico de un espacio de Banach

    OpenAIRE

    Mart??n Su??rez, Miguel

    2000-01-01

    El ??ndice num??rico de un espacio de Banach se define como la mayor constante de equivalencia entre el radio num??rico y la norma usual en el ??lgebra de todos los operadores lineales y continuos sobre ??l. Este concepto fue introducido por G. Lumer en 1968, y estudiado por matem??ticos como F. Bonsall, J. Duncan, C. McGregor, J. Pryce y A. White. En la tesis se hace un estudio sistem??tica de este concepto. Por una parte, se estudia el comportamiento del ??ndice num??ri...

  15. Wiener-Hopf operators on spaces of functions on R+ with values in a Hilbert space

    OpenAIRE

    Petkova, Violeta

    2006-01-01

    A Wiener-Hopf operator on a Banach space of functions on R+ is a bounded operator T such that P^+S_{-a}TS_a=T, for every positive a, where S_a is the operator of translation by a. We obtain a representation theorem for the Wiener-Hopf operators on a large class of functions on R+ with values in a separable Hilbert space.

  16. Smoothness in Banach spaces. Selected problems

    Czech Academy of Sciences Publication Activity Database

    Fabian, Marián; Montesinos, V.; Zizler, Václav

    2006-01-01

    Roč. 100, č. 2 (2006), s. 101-125 ISSN 1578-7303 R&D Projects: GA ČR(CZ) GA201/04/0090; GA AV ČR(CZ) IAA100190610 Institutional research plan: CEZ:AV0Z10190503 Keywords : smooth norm * renorming * weakly compactly generated space Subject RIV: BA - General Mathematics

  17. Ternary Weighted Function and Beurling Ternary Banach Algebra l1ω(S

    Directory of Open Access Journals (Sweden)

    Mehdi Dehghanian

    2011-01-01

    Full Text Available Let S be a ternary semigroup. In this paper, we introduce our notation and prove some elementary properties of a ternary weight function ω on S. Also, we make ternary weighted algebra l1ω(S and show that l1ω(S is a ternary Banach algebra.

  18. Attractor of reaction-diffusion equations in Banach spaces

    Directory of Open Access Journals (Sweden)

    José Valero

    2001-04-01

    Full Text Available In this paper we prove first some abstract theorems on existence of global attractors for differential inclusions generated by w-dissipative operators. Then these results are applied to reaction-diffusion equations in which the Babach space Lp is used as phase space. Finally, new results concerning the fractal dimension of the global attractor in the space L2 are obtained.

  19. On solvability of some quadratic functional-integral equation in Banach algebra

    International Nuclear Information System (INIS)

    Darwish, M.A.

    2007-08-01

    Using the technique of a suitable measure of non-compactness in Banach algebra, we prove an existence theorem for some functional-integral equations which contain, as particular cases, a lot of integral and functional-integral equations that arise in many branches of nonlinear analysis and its applications. Also, the famous Chandrasekhar's integral equation is considered as a special case. (author)

  20. Logarithmic residues of analytic Banach algebra valued functions possessing a simply meromorphic inverse

    NARCIS (Netherlands)

    H. Bart (Harm); T. Ehrhardt; B. Silbermann

    2001-01-01

    textabstractA logarithmic residue is a contour integral of a logarithmic derivative (left or right) of an analytic Banach algebra valued function. For functions possessing a meromorphic inverse with simple poles only, the logarithmic residues are identified as the sums of idempotents. With the help

  1. ON STRONG AND WEAK CONVERGENCE IN n-HILBERT SPACES

    Directory of Open Access Journals (Sweden)

    Agus L. Soenjaya

    2014-03-01

    Full Text Available We discuss the concepts of strong and weak convergence in n-Hilbert spaces and study their properties. Some examples are given to illustrate the concepts. In particular, we prove an analogue of Banach-Saks-Mazur theorem and Radon-Riesz property in the case of n-Hilbert space.

  2. Absolutely continuous measures and compact composition operator on spaces of Cauchy transforms

    Directory of Open Access Journals (Sweden)

    Yusuf Abu Muhanna

    2004-01-01

    Full Text Available The analytic self-map of the unit disk D, φ is said to induce a composition operator Cφ from the Banach space X to the Banach space Y if Cφ(f=f∘φ∈Y for all f∈X. For z∈D and α>0, the families of weighted Cauchy transforms Fα are defined by f(z=∫TKxα(zdμ(x, where μ(x is complex Borel measure, x belongs to the unit circle T, and the kernel Kx(z=(1−x¯z−1. In this paper, we will explore the relationship between the compactness of the composition operator Cφ acting on Fα and the complex Borel measures μ(x.

  3. Optimal Embeddings of Bessel-Potential-Type Spaces into Generalized Hölder Spaces Involving k-Modulus of Smoothness

    Czech Academy of Sciences Publication Activity Database

    Gogatishvili, Amiran; Neves, J. S.; Opic, Bohumír

    2010-01-01

    Roč. 32, č. 3 (2010), s. 201-228 ISSN 0926-2601 R&D Projects: GA ČR GA201/05/2033; GA ČR GA201/08/0383 Institutional research plan: CEZ:AV0Z10190503 Keywords : slowly varying functions * Lorentz-Karamata spaces * Rearrangement-invariant Banach function spaces * Bessel potentials * (fractional) Sobolev-type spaces * Hölder-type spaces * Zygmund-type spaces Subject RIV: BA - General Mathematics Impact factor: 0.853, year: 2010 http://link.springer.com/article/10.1007%2Fs11118-009-9148-2

  4. Amenable crossed product Banach algebras associated with a class of C*-dynamical systems

    NARCIS (Netherlands)

    Jeu, de M.F.E.; Elharti, R.; Pinto, P.R.

    2017-01-01

    We prove that the crossed product Banach algebra ℓ1(G,A;α) that is associated with a C∗-dynamical system (A,G,α) is amenable if G is a discrete amenable group and A is a commutative or finite dimensional C∗-algebra. Perspectives for further developments are indicated.

  5. Lectures given at the Banach Center and C.I.M.E. Joint Summer School

    CERN Document Server

    Lachowicz, Mirosław

    2008-01-01

    The aim of this volume that presents Lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework for the development of a hierarchy of models of complex systems in the natural sciences, with a special attention to Biology and Medicine. Mastering complexity implies sharing different tools requiring much higher level of communication between different mathematical and scientific schools, for solving classes of problems of the same nature. Today more than ever, one of the most important challenges derives from the need to bridge parts of a system evolving at different time and space scales, especially with respect to computational affordability. As a result the content has a rather general character; the main role is played by stochastic processes, positive semigroups, asymptotic analysis, kinetic theory, continuum theory and game theory.

  6. Some remarks on the structure of Lipschitz-free spaces

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr Pavel; Novotný, M.

    2017-01-01

    Roč. 24, č. 2 (2017), s. 283-304 ISSN 1370-1444 R&D Projects: GA ČR GA16-07378S Institutional support: RVO:67985840 Keywords : free Banach space s * compact metric- space s * approximation properties Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.375, year: 2016 https://projecteuclid.org/euclid.bbms/1503453711

  7. Toeplitz Operators, Pseudo-Homogeneous Symbols, and Moment Maps on the Complex Projective Space

    Directory of Open Access Journals (Sweden)

    Miguel Antonio Morales-Ramos

    2017-01-01

    Full Text Available Following previous works for the unit ball due to Nikolai Vasilevski, we define quasi-radial pseudo-homogeneous symbols on the projective space and obtain the corresponding commutativity results for Toeplitz operators. A geometric interpretation of these symbols in terms of moment maps is developed. This leads us to the introduction of a new family of symbols, extended pseudo-homogeneous, that provide larger commutative Banach algebras generated by Toeplitz operators. This family of symbols provides new commutative Banach algebras generated by Toeplitz operators on the unit ball.

  8. The multiplication operators on some analytic function spaces of the ...

    Indian Academy of Sciences (India)

    Given f ∈ E1(Bn) we still denote by f (ξ) (ξ ∈ Sn) its admissible limit at the boundary which exists a.e. A ... BMOA is a Banach space under the following norm: || f ||2 ..... The same inequalities hold when ga is replaced by fa by the same observations. ... The case of the Bloch space and the weighted Bloch space. As in the ...

  9. Sharpness and non-compactness of embeddings of Bessel-potential-type spaces

    Czech Academy of Sciences Publication Activity Database

    Gogatishvili, Amiran; Neves, J. S.; Opic, Bohumír

    2007-01-01

    Roč. 280, č. 10 (2007), s. 1083-1093 ISSN 0025-584X R&D Projects: GA ČR GA201/05/2033 Institutional research plan: CEZ:AV0Z10190503 Keywords : slowly varying functions * Lorentz-Karamata spaces * rearrangement-invariant Banach function spaces Subject RIV: BA - General Mathematics Impact factor: 0.415, year: 2007

  10. On non-archimedean Gurarii spaces

    Czech Academy of Sciences Publication Activity Database

    Kąkol, Jerzy; Kubiś, Wieslaw; Kubzdela, A.

    2017-01-01

    Roč. 450, č. 2 (2017), s. 969-981 ISSN 0022-247X R&D Projects: GA ČR GF16-34860L Institutional support: RVO:67985840 Keywords : isometric embedding * non-Archimedean Banach spaces * universal disposition Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022247X17301051

  11. Isometric Reflection Vectors and Characterizations of Hilbert Spaces

    Directory of Open Access Journals (Sweden)

    Donghai Ji

    2014-01-01

    Full Text Available A known characterization of Hilbert spaces via isometric reflection vectors is based on the following implication: if the set of isometric reflection vectors in the unit sphere SX of a Banach space X has nonempty interior in SX, then X is a Hilbert space. Applying a recent result based on well-known theorem of Kronecker from number theory, we improve this by substantial reduction of the set of isometric reflection vectors needed in the hypothesis.

  12. Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces

    Directory of Open Access Journals (Sweden)

    Flavia Colonna

    2012-01-01

    Full Text Available The logarithmic Bloch space Blog⁡ is the Banach space of analytic functions on the open unit disk 𝔻 whose elements f satisfy the condition ∥f∥=sup⁡z∈𝔻(1-|z|2log⁡  (2/(1-|z|2|f'(z|<∞. In this work we characterize the bounded and the compact weighted composition operators from the Hardy space Hp (with 1≤p≤∞ into the logarithmic Bloch space. We also provide boundedness and compactness criteria for the weighted composition operator mapping Hp into the little logarithmic Bloch space defined as the subspace of Blog⁡ consisting of the functions f such that lim⁡|z|→1(1-|z|2log⁡  (2/(1-|z|2|f'(z|=0.

  13. Integration in Orlicz-Bochner Spaces

    Directory of Open Access Journals (Sweden)

    Marian Nowak

    2018-01-01

    Full Text Available Let (Ω,Σ,μ be a complete σ-finite measure space, φ be a Young function, and X and Y be Banach spaces. Let Lφ(X denote the Orlicz-Bochner space, and Tφ∧ denote the finest Lebesgue topology on Lφ(X. We study the problem of integral representation of (Tφ∧,·Y-continuous linear operators T:Lφ(X→Y with respect to the representing operator-valued measures. The relationships between (Tφ∧,·Y-continuous linear operators T:Lφ(X→Y and the topological properties of their representing operator measures are established.

  14. Tsirelson's space

    CERN Document Server

    Casazza, Peter G

    1989-01-01

    This monograph provides a structure theory for the increasingly important Banach space discovered by B.S. Tsirelson. The basic construction should be accessible to graduate students of functional analysis with a knowledge of the theory of Schauder bases, while topics of a more advanced nature are presented for the specialist. Bounded linear operators are studied through the use of finite-dimensional decompositions, and complemented subspaces are studied at length. A myriad of variant constructions are presented and explored, while open questions are broached in almost every chapter. Two appendices are attached: one dealing with a computer program which computes norms of finitely-supported vectors, while the other surveys recent work on weak Hilbert spaces (where a Tsirelson-type space provides an example).

  15. Two fixed point theorems on quasi-metric spaces via mw- distances

    Energy Technology Data Exchange (ETDEWEB)

    Alegre, C.

    2017-07-01

    In this paper we prove a Banach-type fixed point theorem and a Kannan-type theorem in the setting of quasi-metric spaces using the notion of mw-distance. These theorems generalize some results that have recently appeared in the literature. (Author)

  16. Embeddings of Sobolev-type spaces into generalized Hölder spaces involving k-modulus of smoothness

    Czech Academy of Sciences Publication Activity Database

    Gogatishvili, Amiran; Moura, S.; Neves, J. S.; Opic, B.

    2015-01-01

    Roč. 194, č. 2 (2015), s. 425-450 ISSN 0373-3114 R&D Projects: GA ČR GA13-14743S; GA ČR GA201/08/0383 Institutional support: RVO:67985840 Keywords : rearrangement-invariant Banach function space * modulus of smoothness * distributional gradient Subject RIV: BA - General Mathematics Impact factor: 0.861, year: 2015 http://link.springer.com/article/10.1007/s10231-013-0383-1

  17. Índice numérico de un espacio de Banach

    OpenAIRE

    Martín Suárez, Miguel

    2013-01-01

    El índice numérico de un espacio de Banach se define como la mayor constante de equivalencia entre el radio numérico y la norma usual en el álgebra de todos los operadores lineales y continuos sobre él. Este concepto fue introducido por G. Lumer en 1968, y estudiado por matemáticos como F. Bonsall, J. Duncan, C. McGregor, J. Pryce y A. White. En la tesis se hace un estudio sistemática de este concepto. Por una parte, se estudia el comportamiento del índice numérico respec...

  18. In some symmetric spaces monotonicity properties can be reduced to the cone of rearrangements

    Czech Academy of Sciences Publication Activity Database

    Hudzik, H.; Kaczmarek, R.; Krbec, Miroslav

    2016-01-01

    Roč. 90, č. 1 (2016), s. 249-261 ISSN 0001-9054 Institutional support: RVO:67985840 Keywords : symmetric spaces * K-monotone symmetric Banach spaces * strict monotonicity * lower local uniform monotonicity Subject RIV: BA - General Mathematics Impact factor: 0.826, year: 2016 http://link.springer.com/article/10.1007%2Fs00010-015-0379-6

  19. Asymptotic behaviour of unbounded trajectories for some non-autonomous systems in a Hilbert space

    International Nuclear Information System (INIS)

    Djafari Rouhani, B.

    1990-07-01

    The asymptotic behaviour of unbounded trajectories for non expansive mappings in a real Hilbert space and the extension to more general Banach spaces and to nonlinear contraction semi-group have been studied by many authors. In this paper we study the asymptotic behaviour of unbounded trajectories for a quasi non-autonomous dissipative systems. 26 refs

  20. Fixed Point Theory for Lipschitzian-type Mappings with Applications

    CERN Document Server

    Sahu, D R; Agarwal, Ravi P

    2009-01-01

    Offers a systematic presentation of Lipschitzian-type mappings in metric and Banach spaces. This book covers some basic properties of metric and Banach spaces. It also provides background in terms of convexity, smoothness and geometric coefficients of Banach spaces including duality mappings and metric projection mappings.

  1. Integral type operators from normal weighted Bloch spaces to QT,S spaces

    Directory of Open Access Journals (Sweden)

    Yongyi GU

    2016-08-01

    Full Text Available Operator theory is an important research content of the analytic function space theory. The discussion of simultaneous operator and function space is an effective way to study operator and function space. Assuming that  is an analytic self map on the unit disk Δ, and the normal weighted bloch space μ-B is a Banach space on the unit disk Δ, defining a composition operator C∶C(f=f on μ-B for all f∈μ-B, integral type operator JhC and CJh are generalized by integral operator and composition operator. The boundeness and compactness of the integral type operator JhC acting from normal weighted Bloch spaces to QT,S spaces are discussed, as well as the boundeness of the integral type operators CJh acting from normal weighted Bloch spaces to QT,S spaces. The related sufficient and necessary conditions are given.

  2. On Zweier Sequence Spaces and de la Vall\\'{e}e-Poussin mean of order $\\alpha$

    Directory of Open Access Journals (Sweden)

    Bipan Hazarika

    2016-07-01

    Full Text Available The main purpose of this paper is to study some geometrical properties such as order continuous, the Fatou property and the Banach-Saks property of the new space $[\\mathcal{Z}_{\\lambda}^{\\alpha}]_{\\infty}(p.$

  3. Logarithmic residues of analytic Banach algebra valued functions possessing a simply meromorphic inverse

    OpenAIRE

    Bart, Harm; Ehrhardt, T.; Silbermann, B.

    2001-01-01

    textabstractA logarithmic residue is a contour integral of a logarithmic derivative (left or right) of an analytic Banach algebra valued function. For functions possessing a meromorphic inverse with simple poles only, the logarithmic residues are identified as the sums of idempotents. With the help of this observation, the issue of left versus right logarithmic residues is investigated, both for connected and nonconnected underlying Cauchy domains. Examples are given to elucidate the subject ...

  4. Note on Kadets Klee property and Asplund spaces

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr Pavel; Talponen, J.

    2014-01-01

    Roč. 142, č. 11 (2014), s. 3933-3939 ISSN 0002-9939 R&D Projects: GA ČR(CZ) GAP201/11/0345 Institutional support: RVO:67985840 Keywords : uniformly rotund norms * Banach spaces * sequences Subject RIV: BA - General Mathematics Impact factor: 0.681, year: 2014 http://www.ams.org/journals/proc/2014-142-11/S0002-9939-2014-12123-X/

  5. Introduction to the theory of bases

    CERN Document Server

    Marti, Jürg T

    1969-01-01

    Since the publication of Banach's treatise on the theory of linear operators, the literature on the theory of bases in topological vector spaces has grown enormously. Much of this literature has for its origin a question raised in Banach's book, the question whether every sepa­ rable Banach space possesses a basis or not. The notion of a basis employed here is a generalization of that of a Hamel basis for a finite dimensional vector space. For a vector space X of infinite dimension, the concept of a basis is closely related to the convergence of the series which uniquely correspond to each point of X. Thus there are different types of bases for X, according to the topology imposed on X and the chosen type of convergence for the series. Although almost four decades have elapsed since Banach's query, the conjectured existence of a basis for every separable Banach space is not yet proved. On the other hand, no counter examples have been found to show the existence of a special Banach space having no basis. Howe...

  6. Functional differential equations with unbounded delay in extrapolation spaces

    Directory of Open Access Journals (Sweden)

    Mostafa Adimy

    2014-08-01

    Full Text Available We study the existence, regularity and stability of solutions for nonlinear partial neutral functional differential equations with unbounded delay and a Hille-Yosida operator on a Banach space X. We consider two nonlinear perturbations: the first one is a function taking its values in X and the second one is a function belonging to a space larger than X, an extrapolated space. We use the extrapolation techniques to prove the existence and regularity of solutions and we establish a linearization principle for the stability of the equilibria of our equation.

  7. Greedy Algorithms for Reduced Bases in Banach Spaces

    KAUST Repository

    DeVore, Ronald; Petrova, Guergana; Wojtaszczyk, Przemyslaw

    2013-01-01

    family of PDEs. The performance of this greedy algorithm was initially analyzed in Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) in the case X=H is a Hilbert space. The results of Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) were

  8. An improvement of dimension-free Sobolev imbeddings in r spaces

    Czech Academy of Sciences Publication Activity Database

    Fiorenza, A.; Krbec, Miroslav; Schmeisser, H.-J.

    2014-01-01

    Roč. 267, č. 1 (2014), s. 243-261 ISSN 0022-1236 R&D Projects: GA ČR GAP201/10/1920 Institutional support: RVO:67985840 Keywords : imbedding theorem * small Lebesgue space * rearrangement-invariant Banach Subject RIV: BA - General Mathematics Impact factor: 1.322, year: 2014 http://www.sciencedirect.com/science/article/pii/S0022123614001724

  9. Common fixed points in best approximation for Banach operator pairs with Ciric type I-contractions

    Science.gov (United States)

    Hussain, N.

    2008-02-01

    The common fixed point theorems, similar to those of Ciric [Lj.B. Ciric, On a common fixed point theorem of a Gregus type, Publ. Inst. Math. (Beograd) (N.S.) 49 (1991) 174-178; Lj.B. Ciric, On Diviccaro, Fisher and Sessa open questions, Arch. Math. (Brno) 29 (1993) 145-152; Lj.B. Ciric, On a generalization of Gregus fixed point theorem, Czechoslovak Math. J. 50 (2000) 449-458], Fisher and Sessa [B. Fisher, S. Sessa, On a fixed point theorem of Gregus, Internat. J. Math. Math. Sci. 9 (1986) 23-28], Jungck [G. Jungck, On a fixed point theorem of Fisher and Sessa, Internat. J. Math. Math. Sci. 13 (1990) 497-500] and Mukherjee and Verma [R.N. Mukherjee, V. Verma, A note on fixed point theorem of Gregus, Math. Japon. 33 (1988) 745-749], are proved for a Banach operator pair. As applications, common fixed point and approximation results for Banach operator pair satisfying Ciric type contractive conditions are obtained without the assumption of linearity or affinity of either T or I. Our results unify and generalize various known results to a more general class of noncommuting mappings.

  10. Logarithmic residues and sums of idempotents in the Banach algebra generated by the compact operators and the identity.

    NARCIS (Netherlands)

    H. Bart (Harm); T. Ehrhardt; B. Silbermann

    2001-01-01

    textabstractA logarithmic residue is a contour integral of the (left or right) logarithmic derivative of an analytic Banach algebra valued function. Logarithmic residues are intimately related to sums of idempotents. The present paper is concerned with logarithmic residues and sums of idempotents in

  11. Some Extensions of Banach's Contraction Principle in Complete Cone Metric Spaces

    Directory of Open Access Journals (Sweden)

    Raja P

    2008-01-01

    Full Text Available Abstract In this paper we consider complete cone metric spaces. We generalize some definitions such as -nonexpansive and -uniformly locally contractive functions -closure, -isometric in cone metric spaces, and certain fixed point theorems will be proved in those spaces. Among other results, we prove some interesting applications for the fixed point theorems in cone metric spaces.

  12. Study of localized photon source in space of measures

    International Nuclear Information System (INIS)

    Lisi, M.

    2010-01-01

    In this paper we study a three-dimensional photon transport problem in an interstellar cloud, with a localized photon source inside. The problem is solved indirectly, by defining the adjoint of an operator acting on an appropriate space of continuous functions. By means of sun-adjoint semi groups theory of operators in a Banach space of regular Borel measures, we prove existence and uniqueness of the solution of the problem. A possible approach to identify the localization of the photon source is finally proposed.

  13. Uniqueness of a pre-generator for $C_0$-semigroup on a general locally convex vector space

    OpenAIRE

    Lemle, Ludovic Dan; Wu, Liming

    2007-01-01

    The main purpose is to generalize a theorem of Arendt about uniqueness of $C_0$-semigroups from Banach space setting to the general locally convex vector spaces, more precisely, we show that cores are the only domains of uniqueness for $C_0$-semigroups on locally convex spaces. As an application, we find a necessary and sufficient condition for that the mass transport equation has one unique $L^1(\\R^d,dx)$ weak solution.

  14. Contractive maps on normed linear spaces and their applications to nonlinear matrix equations.

    NARCIS (Netherlands)

    Reurings, M.C.B.

    2017-01-01

    In this paper the author gives necessary and sufficient conditions under which a map is a contraction on a certain subset of a normed linear space. These conditions are already well known for maps on intervals in R. Using the conditions and Banach's fixed point theorem a fixed point theorem can be

  15. Convexity and concavity constants in Lorentz and Marcinkiewicz spaces

    Science.gov (United States)

    Kaminska, Anna; Parrish, Anca M.

    2008-07-01

    We provide here the formulas for the q-convexity and q-concavity constants for function and sequence Lorentz spaces associated to either decreasing or increasing weights. It yields also the formula for the q-convexity constants in function and sequence Marcinkiewicz spaces. In this paper we extent and enhance the results from [G.J.O. Jameson, The q-concavity constants of Lorentz sequence spaces and related inequalities, Math. Z. 227 (1998) 129-142] and [A. Kaminska, A.M. Parrish, The q-concavity and q-convexity constants in Lorentz spaces, in: Banach Spaces and Their Applications in Analysis, Conference in Honor of Nigel Kalton, May 2006, Walter de Gruyter, Berlin, 2007, pp. 357-373].

  16. A fixed point theorem for uniformly locally contractive mappings in a C-chainable cone rectangular metric space

    Directory of Open Access Journals (Sweden)

    Bessem Samet

    2011-09-01

    Full Text Available Recently, Azam, Arshad and Beg [ Banach contraction principle on cone rectangular metric spaces, Appl. Anal. Discrete Math. 2009] introduced the notion of cone rectangular metric spaces by replacing the triangular inequality of a cone metric space by a rectangular inequality. In this paper, we introduce the notion of c-chainable cone rectangular metric space and we establish a fixed point theorem for uniformly locally contractive mappings in such spaces. An example is given to illustrate our obtained result.

  17. The algebraic size of the family of injective operators

    Directory of Open Access Journals (Sweden)

    Bernal-González Luis

    2017-01-01

    Full Text Available In this paper, a criterion for the existence of large linear algebras consisting, except for zero, of one-to-one operators on an infinite dimensional Banach space is provided. As a consequence, it is shown that every separable infinite dimensional Banach space supports a commutative infinitely generated free linear algebra of operators all of whose nonzero members are one-to-one. In certain cases, the assertion holds for nonseparable Banach spaces.

  18. Existence Results for Some Nonlinear Functional-Integral Equations in Banach Algebra with Applications

    Directory of Open Access Journals (Sweden)

    Lakshmi Narayan Mishra

    2016-04-01

    Full Text Available In the present manuscript, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contains various integral and functional equations that considered in nonlinear analysis and its applications. By utilizing the techniques of noncompactness measures, we operate the fixed point theorems such as Darbo's theorem in Banach algebra concerning the estimate on the solutions. The results obtained in this paper extend and improve essentially some known results in the recent literature. We also provide an example of nonlinear functional-integral equation to show the ability of our main result.

  19. Approximation of Müntz-Szász type in weighted spaces

    Energy Technology Data Exchange (ETDEWEB)

    Sedletskii, A M [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

    2013-07-31

    The paper looks at whether a system of exponentials exp(-λ{sub n}t), Reλ{sub n}>0, is complete in various function spaces on the half-line R{sub +}. Wide classes of Banach spaces E and F of functions on R{sub +} are described such that this system is complete in E and F simultaneously. A test is established to determine when this system is complete in the weighted spaces C{sub 0} and L{sup p} with weight (1+t){sup α} on R{sub +}, for α<0 and α<-1, respectively. Bibliography: 18 titles.

  20. Sequential Generalized Transforms on Function Space

    Directory of Open Access Journals (Sweden)

    Jae Gil Choi

    2013-01-01

    Full Text Available We define two sequential transforms on a function space Ca,b[0,T] induced by generalized Brownian motion process. We then establish the existence of the sequential transforms for functionals in a Banach algebra of functionals on Ca,b[0,T]. We also establish that any one of these transforms acts like an inverse transform of the other transform. Finally, we give some remarks about certain relations between our sequential transforms and other well-known transforms on Ca,b[0,T].

  1. A simple proof to an extension of a theorem of A. Pazy in Hilbert space

    International Nuclear Information System (INIS)

    Djafari Rouhani, B.

    1990-08-01

    We prove that if (x n ) n≥0 is a non expansive sequence in a Hilbert space H, the sequence ( n x n ) n≥1 converges strongly in H to the element of minimum norm in the closed convex hull of the sequence (x n+1 -x n ) n≥0 . This result was previously proved; the proof we give here is even much simpler and can be extended to a Banach space. 29 refs

  2. Composition operators on function spaces

    CERN Document Server

    Singh, RK

    1993-01-01

    This volume of the Mathematics Studies presents work done on composition operators during the last 25 years. Composition operators form a simple but interesting class of operators having interactions with different branches of mathematics and mathematical physics. After an introduction, the book deals with these operators on Lp-spaces. This study is useful in measurable dynamics, ergodic theory, classical mechanics and Markov process. The composition operators on functional Banach spaces (including Hardy spaces) are studied in chapter III. This chapter makes contact with the theory of analytic functions of complex variables. Chapter IV presents a study of these operators on locally convex spaces of continuous functions making contact with topological dynamics. In the last chapter of the book some applications of composition operators in isometries, ergodic theory and dynamical systems are presented. An interesting interplay of algebra, topology, and analysis is displayed. This comprehensive and up-to-date stu...

  3. Uniform Convergence and Spectra of Operators in a Class of Fréchet Spaces

    Directory of Open Access Journals (Sweden)

    Angela A. Albanese

    2014-01-01

    Full Text Available Well-known Banach space results (e.g., due to J. Koliha and Y. Katznelson/L. Tzafriri, which relate conditions on the spectrum of a bounded operator T to the operator norm convergence of certain sequences of operators generated by T, are extended to the class of quojection Fréchet spaces. These results are then applied to establish various mean ergodic theorems for continuous operators acting in such Fréchet spaces and which belong to certain operator ideals, for example, compact, weakly compact, and Montel.

  4. Representations for the generalized Drazin inverse of the sum in a Banach algebra and its application for some operator matrices.

    Science.gov (United States)

    Liu, Xiaoji; Qin, Xiaolan

    2015-01-01

    We investigate additive properties of the generalized Drazin inverse in a Banach algebra A. We find explicit expressions for the generalized Drazin inverse of the sum a + b, under new conditions on a, b ∈ A. As an application we give some new representations for the generalized Drazin inverse of an operator matrix.

  5. Elements of mathematics topological vector spaces

    CERN Document Server

    Bourbaki, Nicolas

    2003-01-01

    This is a softcover reprint of the English translation of 1987 of the second edition of Bourbaki's Espaces Vectoriels Topologiques (1981). This second edition is a brand new book and completely supersedes the original version of nearly 30 years ago. But a lot of the material has been rearranged, rewritten, or replaced by a more up-to-date exposition, and a good deal of new material has been incorporated in this book, all reflecting the progress made in the field during the last three decades. Table of Contents. Chapter I: Topological vector spaces over a valued field. Chapter II: Convex sets and locally convex spaces. Chapter III: Spaces of continuous linear mappings. Chapter IV: Duality in topological vector spaces. Chapter V: Hilbert spaces (elementary theory). Finally, there are the usual "historical note", bibliography, index of notation, index of terminology, and a list of some important properties of Banach spaces. (Based on Math Reviews, 1983).

  6. Fixed point theory in metric type spaces

    CERN Document Server

    Agarwal, Ravi P; O’Regan, Donal; Roldán-López-de-Hierro, Antonio Francisco

    2015-01-01

    Written by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is, the text approaches this important area of fixed point analysis beginning from the basic ideas of metric space topology. The text is structured so that it leads the reader from preliminaries and historical notes on metric spaces (in particular G-metric spaces) and on mappings, to Banach type contraction theorems in metric type spaces, fixed point theory in partially ordered G-metric spaces, fixed point theory for expansive mappings in metric type spaces, generalizations, present results and techniques in a very general abstract setting and framework. Fixed point theory is one of the major research areas in nonlinear analysis. This is partly due to the fact that in many real world problems fixed point theory is the basic mathematical tool used to establish the existence of solutions to problems which arise natur...

  7. Local subdifferentials and multivariational inequalities in Banach and Frechet spaces

    Directory of Open Access Journals (Sweden)

    Pavlo O. Kasyanov

    2008-01-01

    Full Text Available Some functional-topological concepts of subdifferential and locally subdifferential maps in Frechet spaces are established. Multivariational inequalities with an operator of the pseudo-monotone type, connected with subdifferential maps, are considered.

  8. Networks for the weak topology of Banach and Fréchet spaces

    Czech Academy of Sciences Publication Activity Database

    Gabriyelyan, S.; Kąkol, Jerzy; Kubiś, Wieslaw; Marciszewski, W.

    2015-01-01

    Roč. 432, č. 2 (2015), s. 1183-1199 ISSN 0022-247X R&D Projects: GA ČR(CZ) GA14-07880S Institutional support: RVO:67985840 Keywords : Fréchet space * space of continuous functions * locally convex space Subject RIV: BA - General Mathematics Impact factor: 1.014, year: 2015 http://www.sciencedirect.com/science/article/pii/S0022247X15006836

  9. Proximinality in generalized direct sums

    Directory of Open Access Journals (Sweden)

    Darapaneni Narayana

    2004-01-01

    Full Text Available We consider proximinality and transitivity of proximinality for subspaces of finite codimension in generalized direct sums of Banach spaces. We give several examples of Banach spaces where proximinality is transitive among subspaces of finite codimension.

  10. Applications of model theory to functional analysis

    CERN Document Server

    Iovino, Jose

    2014-01-01

    During the last two decades, methods that originated within mathematical logic have exhibited powerful applications to Banach space theory, particularly set theory and model theory. This volume constitutes the first self-contained introduction to techniques of model theory in Banach space theory. The area of research has grown rapidly since this monograph's first appearance, but much of this material is still not readily available elsewhere. For instance, this volume offers a unified presentation of Krivine's theorem and the Krivine-Maurey theorem on stable Banach spaces, with emphasis on the

  11. The Quest for the Ultimate Anisotropic Banach Space

    Science.gov (United States)

    Baladi, Viviane

    2017-02-01

    We present a new scale U^{t,s}_p (s1 and -1+1/pBaladi and Tsujii (Ann Inst Fourier 57:127-154, 2007) (or Faure-Roy-Sjöstrand in Open Math J 1:35-81, 2008), the transfer operator acting on U^{t,s}_p can be decomposed into L_{g,b}+L_{g,c}, where L_{g,b} has a controlled norm while a suitable power of L_{g,c} is nuclear. This "nuclear power decomposition" enhances the Lasota-Yorke bounds and makes the spaces U^{t,s}_p amenable to the kneading approach of Milnor-Thurson (Dynamical Systems (Maryland 1986-1987), Springer, Berlin, 1988) (as revisited by Baladi-Ruelle, Baladi in Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps, Monograph, 2016; Baladi and Ruelle in Ergod Theory Dyn Syst 14:621-632, 1994; Baladi and Ruelle in Invent Math 123:553-574, 1996) to study dynamical determinants and zeta functions.

  12. Elements of Hilbert spaces and operator theory

    CERN Document Server

    Vasudeva, Harkrishan Lal

    2017-01-01

    The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compressio...

  13. Global Attractivity Results for Mixed-Monotone Mappings in Partially Ordered Complete Metric Spaces

    Directory of Open Access Journals (Sweden)

    Kalabušić S

    2009-01-01

    Full Text Available We prove fixed point theorems for mixed-monotone mappings in partially ordered complete metric spaces which satisfy a weaker contraction condition than the classical Banach contraction condition for all points that are related by given ordering. We also give a global attractivity result for all solutions of the difference equation , where satisfies mixed-monotone conditions with respect to the given ordering.

  14. Spectral analysis of linear relations and degenerate operator semigroups

    International Nuclear Information System (INIS)

    Baskakov, A G; Chernyshov, K I

    2002-01-01

    Several problems of the spectral theory of linear relations in Banach spaces are considered. Linear differential inclusions in a Banach space are studied. The construction of the phase space and solutions is carried out with the help of the spectral theory of linear relations, ergodic theorems, and degenerate operator semigroups

  15. A note on the m -norm of Chaney-Schaefer | Cullender ...

    African Journals Online (AJOL)

    We give elementary proofs of known results concerning lattice and duality properties of the M-norm, introduced by Chaney and Schaefer, on the tensor product of a Banach space and a Banach lattice. Keywords: Banach lattice; tensor product; Bochner norm. Quaestiones Mathematicae 30(2007), 151–158 ...

  16. The complex structures on the coadjoint orbit spaces of Diff(S1) and on Bers' universal Teichmueller space are compatible

    International Nuclear Information System (INIS)

    Nag, S.; Verjovsky, A.

    1988-08-01

    Precisely two coadjoint orbit spaces of the group of string reparametrizations carry in a natural way the structure of infinite dimensional, holomorphically homogeneous complex manifolds. These are M 1 =Diff(S 1 )/Rot(S 1 ) and M 2 =Diff(S 1 )/Mo-barb(S 1 ). M 2 can be naturally considered as (embedded in) the classical univeral Teichmueller space T(Δ), simply by noting that a diffeomorphism of S 1 is a quasi-symmetric homeomorphism. T(Δ) is itself a homomorphically homogeneous complex Banach manifold. We prove that the inclusion of M 2 in T(Δ) is complex analytic. Every Teichmueller space of finite or infinite dimension is contained canonically and holomorphically in T(Δ). Our result thus appears to connect the loop space approach to bosonic string theory with the sum-over moduli (Polyakov path integral) approach. (author). 12 refs

  17. Bernstein Lethargy Theorem and Reflexivity

    OpenAIRE

    Aksoy, Asuman Güven; Peng, Qidi

    2018-01-01

    In this paper, we prove the equivalence of reflexive Banach spaces and those Banach spaces which satisfy the following form of Bernstein's Lethargy Theorem. Let $X$ be an arbitrary infinite-dimensional Banach space, and let the real-valued sequence $\\{d_n\\}_{n\\ge1}$ decrease to $0$. Suppose that $\\{Y_n\\}_{n\\ge1}$ is a system of strictly nested subspaces of $X$ such that $\\overline Y_n \\subset Y_{n+1}$ for all $n\\ge1$ and for each $n\\ge1$, there exists $y_n\\in Y_{n+1}\\backslash Y_n$ such that ...

  18. Fixed points for some non-obviously contractive operators defined in a space of continuous functions

    OpenAIRE

    C. Avramescu; Cristian Vladimirescu

    2004-01-01

    Let $X$ be an arbitrary (real or complex) Banach space, endowed with the norm $\\left| \\cdot \\right| .$ Consider the space of the continuous functions $C\\left( \\left[ 0,T\\right] ,X\\right) $ $\\left( T>0\\right) $, endowed with the usual topology, and let $M$ be a closed subset of it. One proves that each operator $A:M\\rightarrow M$ fulfilling for all $x,y\\in M$ and for all $t\\in \\left[ 0,T\\right] $ the condition \\begin{eqnarray*} \\left| \\left( Ax\\right) \\left( t\\right) -\\left( Ay\\right) \\l...

  19. The Spaces of Functions of Two Variables of Bounded κΦ-Variation in the Sense of Schramm-Korenblum

    Directory of Open Access Journals (Sweden)

    A. Azócar

    2015-01-01

    Full Text Available The purpose of this paper is twofold. Firstly, we introduce the concept of bounded κΦ-variation in the sense of Schramm-Korenblum for real functions with domain in a rectangle of R2. Secondly, we study some properties of these functions and we prove that the space generated by these functions has a structure of Banach algebra.

  20. On asphericity of convex bodies in linear normed spaces.

    Science.gov (United States)

    Faried, Nashat; Morsy, Ahmed; Hussein, Aya M

    2018-01-01

    In 1960, Dvoretzky proved that in any infinite dimensional Banach space X and for any [Formula: see text] there exists a subspace L of X of arbitrary large dimension ϵ -iometric to Euclidean space. A main tool in proving this deep result was some results concerning asphericity of convex bodies. In this work, we introduce a simple technique and rigorous formulas to facilitate calculating the asphericity for each set that has a nonempty boundary set with respect to the flat space generated by it. We also give a formula to determine the center and the radius of the smallest ball containing a nonempty nonsingleton set K in a linear normed space, and the center and the radius of the largest ball contained in it provided that K has a nonempty boundary set with respect to the flat space generated by it. As an application we give lower and upper estimations for the asphericity of infinite and finite cross products of these sets in certain spaces, respectively.

  1. The τ-fixed point property for nonexpansive mappings

    Directory of Open Access Journals (Sweden)

    Tomás Domínguez Benavides

    1998-01-01

    conditions, we show that normal structure assures the τ-FPP and Goebel-Karlovitz's Lemma still holds. We use this results to study two geometrical properties which imply the τ-FPP: the τ-GGLD and M(τ properties. We show several examples of spaces and topologies where these results can be applied, specially the topology of convergence locally in measure in Lebesgue spaces. In the second part we study the preservence of the τ-FPP under isomorphisms. In order to do that we study some geometric constants for a Banach space X such that the τ-FPP is shared by any isomorphic Banach space Y satisfying that the Banach-Mazur distance between X and Y is less than some of these constants.

  2. Differential calculus in normed linear spaces

    CERN Document Server

    Mukherjea, Kalyan

    2007-01-01

    This book presents Advanced Calculus from a geometric point of view: instead of dealing with partial derivatives of functions of several variables, the derivative of the function is treated as a linear transformation between normed linear spaces. Not only does this lead to a simplified and transparent exposition of "difficult" results like the Inverse and Implicit Function Theorems but also permits, without any extra effort, a discussion of the Differential Calculus of functions defined on infinite dimensional Hilbert or Banach spaces.The prerequisites demanded of the reader are modest: a sound understanding of convergence of sequences and series of real numbers, the continuity and differentiability properties of functions of a real variable and a little Linear Algebra should provide adequate background for understanding the book. The first two chapters cover much of the more advanced background material on Linear Algebra (like dual spaces, multilinear functions and tensor products.) Chapter 3 gives an ab ini...

  3. A note on convex renorming and fragmentability

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    Abstract. Using the game approach to fragmentability, we give new and simpler proofs of the following known results: (a) If the Banach space admits an equivalent. Kadec norm, then its weak topology is fragmented by a metric which is stronger than the norm topology. (b) If the Banach space admits an equivalent rotund ...

  4. A note on biorthogonal systems in weakly compactly generated Banach spaces

    Czech Academy of Sciences Publication Activity Database

    Fabian, Marián; Gonzáles, A.; Montesinos, V.

    2009-01-01

    Roč. 34, č. 2 (2009), s. 555-564 ISSN 1239-629X R&D Projects: GA AV ČR(CZ) IAA100190610 Institutional research plan: CEZ:AV0Z10190503 Keywords : weakly compactly generated (sub)space * projectional resolution * fundamental biorthogonal system Subject RIV: BA - General Mathematics Impact factor: 0.539, year: 2009

  5. Convergence theorems for quasi-contractive maps in uniformly convex spaces

    International Nuclear Information System (INIS)

    Chidume, C.E.; Osilike, M.O.

    1992-04-01

    Let K be a nonempty closed convex and bounded subset of a real uniformly convex Banach space E of modulus of convexity of power type q≥2. Let T by a quasi-contractive mapping of K into itself. It is proved that each of two well known fixed point iteration methods (the Mann and the Ishikawa iteration methods) converges strongly, without any compactness assumption on the domain of the map, to the unique fixed point of T in K. Our theorems generalize important known results. (author). 22 refs

  6. Interpolation functors and interpolation spaces

    CERN Document Server

    Brudnyi, Yu A

    1991-01-01

    The theory of interpolation spaces has its origin in the classical work of Riesz and Marcinkiewicz but had its first flowering in the years around 1960 with the pioneering work of Aronszajn, Calderón, Gagliardo, Krein, Lions and a few others. It is interesting to note that what originally triggered off this avalanche were concrete problems in the theory of elliptic boundary value problems related to the scale of Sobolev spaces. Later on, applications were found in many other areas of mathematics: harmonic analysis, approximation theory, theoretical numerical analysis, geometry of Banach spaces, nonlinear functional analysis, etc. Besides this the theory has a considerable internal beauty and must by now be regarded as an independent branch of analysis, with its own problems and methods. Further development in the 1970s and 1980s included the solution by the authors of this book of one of the outstanding questions in the theory of the real method, the K-divisibility problem. In a way, this book harvests the r...

  7. On the Maximal Ideals of Non-Zero-Symmetric Near-Rings and of ...

    African Journals Online (AJOL)

    Keywords: ideals, near-rings, algebra, composition algebras, polynomial functions, Ω-groups, maximal ideals, Brown-McCoy radical, operations, polynomials, primal algebras, ordinary polynomial rings, skew polynomial rings, semigroup rings, Banach, banach space, Pettis, Pettis integrable, complete, congruences, ...

  8. Additive subgroups of topological vector spaces

    CERN Document Server

    Banaszczyk, Wojciech

    1991-01-01

    The Pontryagin-van Kampen duality theorem and the Bochner theorem on positive-definite functions are known to be true for certain abelian topological groups that are not locally compact. The book sets out to present in a systematic way the existing material. It is based on the original notion of a nuclear group, which includes LCA groups and nuclear locally convex spaces together with their additive subgroups, quotient groups and products. For (metrizable, complete) nuclear groups one obtains analogues of the Pontryagin duality theorem, of the Bochner theorem and of the Lévy-Steinitz theorem on rearrangement of series (an answer to an old question of S. Ulam). The book is written in the language of functional analysis. The methods used are taken mainly from geometry of numbers, geometry of Banach spaces and topological algebra. The reader is expected only to know the basics of functional analysis and abstract harmonic analysis.

  9. Theory of linear operations

    CERN Document Server

    Banach, S

    1987-01-01

    This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra.The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series.A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'''') complements this important monograph.

  10. Strong Convergence of Monotone Hybrid Method for Maximal Monotone Operators and Hemirelatively Nonexpansive Mappings

    Directory of Open Access Journals (Sweden)

    Chakkrid Klin-eam

    2009-01-01

    Full Text Available We prove strong convergence theorems for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a hemirelatively nonexpansive mapping in a Banach space by using monotone hybrid iteration method. By using these results, we obtain new convergence results for resolvents of maximal monotone operators and hemirelatively nonexpansive mappings in a Banach space.

  11. An iterative method for nonlinear demiclosed monotone-type operators

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1991-01-01

    It is proved that a well known fixed point iteration scheme which has been used for approximating solutions of certain nonlinear demiclosed monotone-type operator equations in Hilbert spaces remains applicable in real Banach spaces with property (U, α, m+1, m). These Banach spaces include the L p -spaces, p is an element of [2,∞]. An application of our results to the approximation of a solution of a certain linear operator equation in this general setting is also given. (author). 19 refs

  12. Banach spaces with projectional skeletons

    Czech Academy of Sciences Publication Activity Database

    Kubiś, Wieslaw

    2009-01-01

    Roč. 350, č. 2 (2009), s. 758-776 ISSN 0022-247X Institutional research plan: CEZ:AV0Z10190503 Keywords : projection * projectional skeleton * norming set Subject RIV: BA - General Mathematics Impact factor: 1.225, year: 2009

  13. The Maslov index in weak symplectic functional analysis

    DEFF Research Database (Denmark)

    Booss-Bavnbek, Bernhelm; Zhu, Chaofeng

    2013-01-01

    We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach...

  14. The coadjoint orbit spaces of Diff(S1) and Teichmueller spaces

    International Nuclear Information System (INIS)

    Nag, S.; Verjovsky, A.

    1989-09-01

    Precisely two of the homogeneous spaces that appear as coadjoint orbits of the group of string reparametrizations (Diff (S 1 )) carry in a natural way the structure of infinite dimensional, holomorphically homogeneous complex analytic Kaehler manifolds. These are N = Diff (S 1 )/Rot (S 1 ) and M = Diff (S 1 )/Moeb (S 1 ). Note that N is a holomorphic disc fiber space over M. Now, M can be naturally considered as embedded in the classical universal Teichmueller space T(1), simply by noting that a diffeomorphism of S 1 is a quasisymmetric homeomorphism. T(1) is itself a homomorphically homogeneous complex Banach manifold. We prove in the first part of the paper that the inclusion of M in T(1) is complex analytic. In the latter portion of this paper it is shown that the unique homogeneous Kaehler metric carried by M = Diff (S 1 )/SL(2, R) induces precisely the Weil-Petersson metric on the Teichmueller space. This is via our identification of M as a holomorphic submanifold of universal Teichmueller space. Now recall that every Teichmueller space T(G) of finite or infinite dimension is contained canonically and holomorphically within T(1). Our computations allow us also to prove that every T(G), G any infinite Fuchsian group, projects out of M transversely. This last assertion is related to the ''fractal'' nature of G-invariant quasicircles, and to Mostow rigidity on the line. Our results thus connect the loop space approach to bosonic string theory with the sumover moduli (Polyakov path integral) approach. (author). 21 refs

  15. Spectral analysis of difference and differential operators in weighted spaces

    International Nuclear Information System (INIS)

    Bichegkuev, M S

    2013-01-01

    This paper is concerned with describing the spectrum of the difference operator K:l α p (Z,X)→l α p (Z......athscrKx)(n)=Bx(n−1),  n∈Z,  x∈l α p (Z,X), with a constant operator coefficient B, which is a bounded linear operator in a Banach space X. It is assumed that K acts in the weighted space l α p (Z,X), 1≤p≤∞, of two-sided sequences of vectors from X. The main results are obtained in terms of the spectrum σ(B) of the operator coefficient B and properties of the weight function. Applications to the study of the spectrum of a differential operator with an unbounded operator coefficient (the generator of a strongly continuous semigroup of operators) in weighted function spaces are given. Bibliography: 23 titles

  16. On the factorization of integral operators on spaces of summable functions

    International Nuclear Information System (INIS)

    Engibaryan, Norayr B

    2009-01-01

    We consider the factorization I-K=(I-U + )(I-U - ), where I is the identity operator, K is an integral operator acting on some Banach space of functions summable with respect to a measure μ on (a,b) subset of (-∞,+∞) continuous relative to the Lebesgue measure, (Kf)(x)=∫ a b k(x,t)f(t)μ(dt), x element of (a,b), and U ± are the desired Volterra operators. A necessary and sufficient condition is found for the existence of this factorization for a rather wide class of operators K with positive kernels and for Hilbert-Schmidt operators.

  17. Mutational analysis a joint framework for Cauchy problems in and beyond vector spaces

    CERN Document Server

    Lorenz, Thomas

    2010-01-01

    Ordinary differential equations play a central role in science and have been extended to evolution equations in Banach spaces. For many applications, however, it is difficult to specify a suitable normed vector space. Shapes without a priori restrictions, for example, do not have an obvious linear structure. This book generalizes ordinary differential equations beyond the borders of vector spaces with a focus on the well-posed Cauchy problem in finite time intervals. Here are some of the examples: - Feedback evolutions of compact subsets of the Euclidean space - Birth-and-growth processes of random sets (not necessarily convex) - Semilinear evolution equations - Nonlocal parabolic differential equations - Nonlinear transport equations for Radon measures - A structured population model - Stochastic differential equations with nonlocal sample dependence and how they can be coupled in systems immediately - due to the joint framework of Mutational Analysis. Finally, the book offers new tools for modelling.

  18. Convergence theorems for quasi-contractive mappings

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1992-01-01

    It is proved that each of two well known fixed point iteration methods (the Mann and Ishikawa iteration methods) converges strongly, without any compactness assumption on the domain of the map, to the unique fixed point of a quasi-contractive map in real Banach spacers with property (U, α, m+1, m). These Banach spaces include the L p (or l p ) spaces, p ≥ 2. Our theorems generalize important known results. (author). 29 refs

  19. Application of the Banach Fixed-Point Theorem to the Scattering Problem at a Nonlinear Three-Layer Structure with Absorption

    Directory of Open Access Journals (Sweden)

    V. S. Serov

    2010-01-01

    Full Text Available A method based on the Banach fixed-point theorem is proposed for obtaining certain solutions (TE-polarized electromagnetic waves of the Helmholtz equation describing the reflection and transmission of a plane monochromatic wave at a nonlinear lossy dielectric film situated between two lossless linear semiinfinite media. All three media are assumed to be nonmagnetic and isotropic. The permittivity of the film is modelled by a continuously differentiable function of the transverse coordinate with a saturating Kerr nonlinearity. It is shown that the solution of the Helmholtz equation exists in form of a uniformly convergent sequence of iterations of the equivalent Volterra integral equation. Numerical results are presented.

  20. Relativistic helicity and link in Minkowski space-time

    International Nuclear Information System (INIS)

    Yoshida, Z.; Kawazura, Y.; Yokoyama, T.

    2014-01-01

    A relativistic helicity has been formulated in the four-dimensional Minkowski space-time. Whereas the relativistic distortion of space-time violates the conservation of the conventional helicity, the newly defined relativistic helicity conserves in a barotropic fluid or plasma, dictating a fundamental topological constraint. The relation between the helicity and the vortex-line topology has been delineated by analyzing the linking number of vortex filaments which are singular differential forms representing the pure states of Banach algebra. While the dimension of space-time is four, vortex filaments link, because vorticities are primarily 2-forms and the corresponding 2-chains link in four dimension; the relativistic helicity measures the linking number of vortex filaments that are proper-time cross-sections of the vorticity 2-chains. A thermodynamic force yields an additional term in the vorticity, by which the vortex filaments on a reference-time plane are no longer pure states. However, the vortex filaments on a proper-time plane remain to be pure states, if the thermodynamic force is exact (barotropic), thus, the linking number of vortex filaments conserves

  1. Perturbation Results on Semi-Fredholm Operators and Applications

    Directory of Open Access Journals (Sweden)

    Abdelmoumen Boulbeba

    2009-01-01

    Full Text Available We give some results concerning stability in the Fredholm operators and Browder operators set, via the concept of measure of noncompactness. Moreover, we prove some localization results on the essential spectra of bounded operators on Banach space. As application, we describe the essential spectra of weighted shift operators. Finally, we describe the spectra of polynomially compact operators, and we use the obtained results to study the solvability for operator equations in Banach spaces.

  2. Existence and decay of solutions of some nonlinear parabolic variational inequalities

    Directory of Open Access Journals (Sweden)

    Mitsuhiro Nakao

    1980-01-01

    Full Text Available This paper discusses the existence and decay of solutions u(t of the variational inequality of parabolic type: ≧0for ∀v∈Lp([0,∞;V(p≧2 with v(t∈K a.e. in [0,∞, where K is a closed convex set of a separable uniformly convex Banach space V, A is a nonlinear monotone operator from V to V* and B is a nonlinear operator from Banach space W to W*. V and W are related as V⊂W⊂H for a Hilbert space H. No monotonicity assumption is made on B.

  3. Scattering theory of the linear Boltzmann operator

    International Nuclear Information System (INIS)

    Hejtmanek, J.

    1975-01-01

    In time dependent scattering theory we know three important examples: the wave equation around an obstacle, the Schroedinger and the Dirac equation with a scattering potential. In this paper another example from time dependent linear transport theory is added and considered in full detail. First the linear Boltzmann operator in certain Banach spaces is rigorously defined, and then the existence of the Moeller operators is proved by use of the theorem of Cook-Jauch-Kuroda, that is generalized to the case of a Banach space. (orig.) [de

  4. Convex analysis and monotone operator theory in Hilbert spaces

    CERN Document Server

    Bauschke, Heinz H

    2017-01-01

    This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, ma...

  5. Generalized monotone operators in Banach spaces

    International Nuclear Information System (INIS)

    Nanda, S.

    1988-07-01

    The concept of F-monotonicity was first introduced by Kato and this generalizes the notion of monotonicity introduced by Minty. The purpose of this paper is to define various types of F-monotonicities and discuss the relationships among them. (author). 6 refs

  6. Generalized Mann Iterations for Approximating Fixed Points of a Family of Hemicontractions

    Directory of Open Access Journals (Sweden)

    Jin Liang

    2008-06-01

    Full Text Available This paper concerns common fixed points for a finite family of hemicontractions or a finite family of strict pseudocontractions on uniformly convex Banach spaces. By introducing a new iteration process with error term, we obtain sufficient and necessary conditions, as well as sufficient conditions, for the existence of a fixed point. As one will see, we derive these strong convergence theorems in uniformly convex Banach spaces and without any requirement of the compactness on the domain of the mapping. The results given in this paper extend some previous theorems.

  7. First Meeting in Topology and Functional Analysis

    CERN Document Server

    López-Pellicer, Manuel

    2014-01-01

    Descriptive topology and functional analysis, with extensive material demonstrating new connections between them, are the subject of the first section of this work. Applications to spaces of continuous functions, topological Abelian groups, linear topological equivalence and to the separable quotient problem are included and are presented as open problems. The second section is devoted to Banach spaces, Banach algebras and operator theory. Each chapter presents a lot of worthwhile and important recent theorems with an abstract discussing the material in the chapter. Each chapter can almost be seen as a survey covering a particular area.

  8. Convergence theorems for certain classes of nonlinear mappings

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1992-01-01

    Recently, Xinlong Weng announced a convergence theorem for the iterative approximation of fixed points of local strictly pseudo-contractive mappings in uniformly smooth Banach spaces, (Proc. Amer. Math. Soc. Vol.113, No.3 (1991) 727-731). An example is presented which shows that this theorem of Weng is false. Then, a convergence theorem is proved, in certain real Banach spaces, for approximation a solution of the inclusion f is an element of x + Tx, where T is a set-valued monotone operator. An explicit error estimate is also presented. (author). 26 refs

  9. Local relativistic invariant flows for quantum fields

    International Nuclear Information System (INIS)

    Albeverio, S.; Hoeegh-Krahn, R.; Sirugue, M.

    1983-01-01

    For quantum fields with trigonometric interaction in arbitrary space dimension we construct a representation of the Lorentz group by automorphisms on a Banach space generated by the Weyl algebra. (orig.)

  10. Convergence rates in constrained Tikhonov regularization: equivalence of projected source conditions and variational inequalities

    International Nuclear Information System (INIS)

    Flemming, Jens; Hofmann, Bernd

    2011-01-01

    In this paper, we enlighten the role of variational inequalities for obtaining convergence rates in Tikhonov regularization of nonlinear ill-posed problems with convex penalty functionals under convexity constraints in Banach spaces. Variational inequalities are able to cover solution smoothness and the structure of nonlinearity in a uniform manner, not only for unconstrained but, as we indicate, also for constrained Tikhonov regularization. In this context, we extend the concept of projected source conditions already known in Hilbert spaces to Banach spaces, and we show in the main theorem that such projected source conditions are to some extent equivalent to certain variational inequalities. The derived variational inequalities immediately yield convergence rates measured by Bregman distances

  11. Convergence theorems for strictly hemi-contractive maps

    International Nuclear Information System (INIS)

    Chidume, C.E.; Osilike, M.O.

    1992-04-01

    It is proved that each of two well-known fixed point iteration methods (the Mann and the Ishikawa iteration methods) converges strongly to the fixed point of strictly hemi-contractive map in real Banach spaces with property (U, λ, m+1,m), λ is an element of R, m is an element of IN. The class of strictly hemi-contractive maps includes all strictly pseudo-contractive maps with nonempty fixed point sets; and Banach spaces with property (U, λ, m+1, m), λ is an element of R, m is an element of IN include the L p (or l p ) spaces, p≥2. Our theorems generalize important known results. (author). 22 refs

  12. Conference on Abstract Spaces and Approximation

    CERN Document Server

    Szökefalvi-Nagy, B; Abstrakte Räume und Approximation; Abstract spaces and approximation

    1969-01-01

    The present conference took place at Oberwolfach, July 18-27, 1968, as a direct follow-up on a meeting on Approximation Theory [1] held there from August 4-10, 1963. The emphasis was on theoretical aspects of approximation, rather than the numerical side. Particular importance was placed on the related fields of functional analysis and operator theory. Thirty-nine papers were presented at the conference and one more was subsequently submitted in writing. All of these are included in these proceedings. In addition there is areport on new and unsolved problems based upon a special problem session and later communications from the partici­ pants. A special role is played by the survey papers also presented in full. They cover a broad range of topics, including invariant subspaces, scattering theory, Wiener-Hopf equations, interpolation theorems, contraction operators, approximation in Banach spaces, etc. The papers have been classified according to subject matter into five chapters, but it needs littl...

  13. Homology of normal chains and cohomology of charges

    CERN Document Server

    Pauw, Th De; Pfeffer, W F

    2017-01-01

    The authors consider a category of pairs of compact metric spaces and Lipschitz maps where the pairs satisfy a linearly isoperimetric condition related to the solvability of the Plateau problem with partially free boundary. It includes properly all pairs of compact Lipschitz neighborhood retracts of a large class of Banach spaces. On this category the authors define homology and cohomology functors with real coefficients which satisfy the Eilenberg-Steenrod axioms, but reflect the metric properties of the underlying spaces. As an example they show that the zero-dimensional homology of a space in our category is trivial if and only if the space is path connected by arcs of finite length. The homology and cohomology of a pair are, respectively, locally convex and Banach spaces that are in duality. Ignoring the topological structures, the homology and cohomology extend to all pairs of compact metric spaces. For locally acyclic spaces, the authors establish a natural isomorphism between their cohomology and the �...

  14. Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras

    Directory of Open Access Journals (Sweden)

    Lothar Schlafer

    2008-05-01

    Full Text Available C*-algebraic Weyl quantization is extended by allowing also degenerate pre-symplectic forms for the Weyl relations with infinitely many degrees of freedom, and by starting out from enlarged classical Poisson algebras. A powerful tool is found in the construction of Poisson algebras and non-commutative twisted Banach-*-algebras on the stage of measures on the not locally compact test function space. Already within this frame strict deformation quantization is obtained, but in terms of Banach-*-algebras instead of C*-algebras. Fourier transformation and representation theory of the measure Banach-*-algebras are combined with the theory of continuous projective group representations to arrive at the genuine C*-algebraic strict deformation quantization in the sense of Rieffel and Landsman. Weyl quantization is recognized to depend in the first step functorially on the (in general infinite dimensional, pre-symplectic test function space; but in the second step one has to select a family of representations, indexed by the deformation parameter h. The latter ambiguity is in the present investigation connected with the choice of a folium of states, a structure, which does not necessarily require a Hilbert space representation.

  15. Eigenvalues, embeddings and generalised trigonometric functions

    CERN Document Server

    Lang, Jan

    2011-01-01

    The main theme of the book is the study, from the standpoint of s-numbers, of integral operators of Hardy type and related Sobolev embeddings. In the theory of s-numbers the idea is to attach to every bounded linear map between Banach spaces a monotone decreasing sequence of non-negative numbers with a view to the classification of operators according to the way in which these numbers approach a limit: approximation numbers provide an especially important example of such numbers. The asymptotic behavior of the s-numbers of Hardy operators acting between Lebesgue spaces is determined here in a wide variety of cases. The proof methods involve the geometry of Banach spaces and generalized trigonometric functions; there are connections with the theory of the p-Laplacian.

  16. The Maslov index in symplectic Banach spaces

    DEFF Research Database (Denmark)

    Booss-Bavnbek, Bernhelm; Zhu, Chaofeng

    . Using such decompositions the authors define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. The authors prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction while recovering all...... for varying well-posed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral flow on partitioned manifolds....

  17. Regularity of difference equations on Banach spaces

    CERN Document Server

    Agarwal, Ravi P; Lizama, Carlos

    2014-01-01

    This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevant results. They address recent advances in the field, as well as basic semigroup and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research. This book is intended for graduate students and researchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis.

  18. Contractive type non-self mappings on metric spaces of hyperbolic type

    Science.gov (United States)

    Ciric, Ljubomir B.

    2006-05-01

    Let (X,d) be a metric space of hyperbolic type and K a nonempty closed subset of X. In this paper we study a class of mappings from K into X (not necessarily self-mappings on K), which are defined by the contractive condition (2.1) below, and a class of pairs of mappings from K into X which satisfy the condition (2.28) below. We present fixed point and common fixed point theorems which are generalizations of the corresponding fixed point theorems of Ciric [L.B. Ciric, Quasi-contraction non-self mappings on Banach spaces, Bull. Acad. Serbe Sci. Arts 23 (1998) 25-31; L.B. Ciric, J.S. Ume, M.S. Khan, H.K.T. Pathak, On some non-self mappings, Math. Nachr. 251 (2003) 28-33], Rhoades [B.E. Rhoades, A fixed point theorem for some non-self mappings, Math. Japon. 23 (1978) 457-459] and many other authors. Some examples are presented to show that our results are genuine generalizations of known results from this area.

  19. A new approach to the existence of zeros for nonlinear operators

    Directory of Open Access Journals (Sweden)

    Paolo Cubiotti

    1994-11-01

    Full Text Available In this paper we present a necessary and sufficient condition for the existence of zeros for a nonlinear operator from a compact topological space into the topological dual of a real Banach space. Some applications are derived.

  20. Projection-iteration methods for solving nonlinear operator equations

    International Nuclear Information System (INIS)

    Nguyen Minh Chuong; Tran thi Lan Anh; Tran Quoc Binh

    1989-09-01

    In this paper, the authors investigate a nonlinear operator equation in uniformly convex Banach spaces as in metric spaces by using stationary and nonstationary generalized projection-iteration methods. Convergence theorems in the strong and weak sense were established. (author). 7 refs

  1. Proceedings – Mathematical Sciences | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    In this paper, we study the noncommutative Orlicz space L φ ( M ~ , τ ) ,which generalizes the concept of noncommutative L p space, where M is a von Neumann algebra, and φ is an Orlicz function. As a modular space, the space L φ ( M ~ , τ ) possesses the Fatou property, and consequently, it is a Banach space. In addition ...

  2. Abstract structure of partial function $*$-algebras over semi-direct product of locally compact groups

    Directory of Open Access Journals (Sweden)

    Arash Ghaani Farashahi

    2015-12-01

    Full Text Available This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-convolution on $L^1(G_tau$ and we show that, with respect to each of them, the function space $L^1(G_tau$ is a Banach algebra. We define $tau$-convolution as a linear combination of the left and right $tau$-convolution and we show that the $tau$-convolution is commutative if and only if $K$ is abelian. We prove that there is a $tau$-involution on $L^1(G_tau$ such that with respect to the $tau$-involution and $tau$-convolution, $L^1(G_tau$ is a non-associative Banach $*$-algebra. It is also shown that when $K$ is abelian, the $tau$-involution and $tau$-convolution make $L^1(G_tau$ into a Jordan Banach $*$-algebra. Finally, we also present the generalized notation of $tau$-convolution for other $L^p$-spaces with $p>1$.

  3. Dynamical zeta functions and dynamical determinants for hyperbolic maps a functional approach

    CERN Document Server

    Baladi, Viviane

    2018-01-01

    The spectra of transfer operators associated to dynamical systems, when acting on suitable Banach spaces, contain key information about the ergodic properties of the systems. Focusing on expanding and hyperbolic maps, this book gives a self-contained account on the relation between zeroes of dynamical determinants, poles of dynamical zeta functions, and the discrete spectra of the transfer operators. In the hyperbolic case, the first key step consists in constructing a suitable Banach space of anisotropic distributions. The first part of the book is devoted to the easier case of expanding endomorphisms, showing how the (isotropic) function spaces relevant there can be studied via Paley–Littlewood decompositions, and allowing easier access to the construction of the anisotropic spaces which is performed in the second part. This is the first book describing the use of anisotropic spaces in dynamics. Aimed at researchers and graduate students, it presents results and techniques developed since the beginning of...

  4. Iterative approximation of the solution of a monotone operator equation in certain Banach spaces

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1988-01-01

    Let X=L p (or l p ), p ≥ 2. The solution of the equation Ax=f, f is an element of X is approximated in X by an iteration process in each of the following two cases: (i) A is a bounded linear mapping of X into itself which is also bounded below; and, (ii) A is a nonlinear Lipschitz mapping of X into itself and satisfies ≥ m |x-y| 2 , for some constant m > 0 and for all x, y in X, where j is the single-valued normalized duality mapping of X into X* (the dual space of X). A related result deals with the iterative approximation of the fixed point of a Lipschitz strictly pseudocontractive mapping in X. (author). 12 refs

  5. Mathematical analysis of an age-structured population model with space-limited recruitment.

    Science.gov (United States)

    Kamioka, Katumi

    2005-11-01

    In this paper, we investigate structured population model of marine invertebrate whose life stage is composed of sessile adults and pelagic larvae, such as barnacles contained in a local habitat. First we formulate the basic model as an Cauchy problem on a Banach space to discuss the existence and uniqueness of non-negative solution. Next we define the basic reproduction number R0 to formulate the invasion condition under which the larvae can successfully settle down in the completely vacant habitat. Subsequently we examine existence and stability of steady states. We show that the trivial steady state is globally asymptotically stable if R0 1. Furthermore, we show that a positive (non-trivial) steady state uniquely exists if R0 > 1 and it is locally asymptotically stable as far as absolute value of R0 - 1 is small enough.

  6. Iterative methods for nonlinear set-valued operators of the monotone type with applications to operator equations

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1989-06-01

    The fixed points of set-valued operators satisfying a condition of monotonicity type in real Banach spaces with uniformly convex dual spaces are approximated by recursive averaging processes. Applications to important classes of linear and nonlinear operator equations are also presented. (author). 33 refs

  7. An introduction to nonlinear analysis and fixed point theory

    CERN Document Server

    Pathak, Hemant Kumar

    2018-01-01

    This book systematically introduces the theory of nonlinear analysis, providing an overview of topics such as geometry of Banach spaces, differential calculus in Banach spaces, monotone operators, and fixed point theorems. It also discusses degree theory, nonlinear matrix equations, control theory, differential and integral equations, and inclusions. The book presents surjectivity theorems, variational inequalities, stochastic game theory and mathematical biology, along with a large number of applications of these theories in various other disciplines. Nonlinear analysis is characterised by its applications in numerous interdisciplinary fields, ranging from engineering to space science, hydromechanics to astrophysics, chemistry to biology, theoretical mechanics to biomechanics and economics to stochastic game theory. Organised into ten chapters, the book shows the elegance of the subject and its deep-rooted concepts and techniques, which provide the tools for developing more realistic and accurate models for ...

  8. Impulsive moving mirror model and the stability of Schroedinger equation with impulse effect in a Banach space

    International Nuclear Information System (INIS)

    Kostadinov, S.I.; Petrov, G.

    1992-01-01

    From a special class of systems has been used a Schroedinger equation with impulse effect in Minkowski space field theory with time dependent boundary conditions, i.e. those of moving mirrors. The field theoretical approach for studying the properties of the vacuum starts from an analysis of the behaviour of local field quantities in Minkowski space with uniformly moving mirrors. For the impulsive moving mirror model is the real process of interaction between the quantum field and the external mirror a subject to disturbances in its evolution acting in time very short compared with the entire duration of the process. So the stability of the solution of the Schroedinger evolution equation for the process in the stability of the vacuum of Casimir. 8 refs

  9. Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators

    Directory of Open Access Journals (Sweden)

    Allaberen Ashyralyev

    2014-01-01

    Full Text Available The nonlocal boundary value problem for the parabolic differential equation v'(t+A(tv(t=f(t  (0≤t≤T,  v(0=v(λ+φ,  0<λ≤T in an arbitrary Banach space E with the dependent linear positive operator A(t is investigated. The well-posedness of this problem is established in Banach spaces C0β,γ(Eα-β of all Eα-β-valued continuous functions φ(t on [0,T] satisfying a Hölder condition with a weight (t+τγ. New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.

  10. Functional analysis and applied optimization in Banach spaces applications to non-convex variational models

    CERN Document Server

    Botelho, Fabio

    2014-01-01

    This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.

  11. Finite-dimensional approximation for operator equations of Hammerstein type

    International Nuclear Information System (INIS)

    Buong, N.

    1992-11-01

    The purpose of this paper is to establish convergence rate for a method of finite-dimensional approximation to solve operator equation of Hammerstein type in real reflexive Banach space. In order to consider a numerical example an iteration method is proposed in Hilbert space. (author). 25 refs

  12. Minimizing convex functions by continuous descent methods

    Directory of Open Access Journals (Sweden)

    Sergiu Aizicovici

    2010-01-01

    Full Text Available We study continuous descent methods for minimizing convex functions, defined on general Banach spaces, which are associated with an appropriate complete metric space of vector fields. We show that there exists an everywhere dense open set in this space of vector fields such that each of its elements generates strongly convergent trajectories.

  13. Winter School on Operator Spaces, Noncommutative Probability and Quantum Groups

    CERN Document Server

    2017-01-01

    Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems.  A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions.  The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory of Banach spaces to quantum information. The l...

  14. Impulsive evolution inclusions with infinite delay and multivalued jumps

    Directory of Open Access Journals (Sweden)

    Mouffak Benchohra

    2012-08-01

    Full Text Available In this paper we prove the existence of a mild solution for a class of impulsive semilinear evolution differential inclusions with infinite delay and multivalued jumps in a Banach space.

  15. Convergence theorems for mappings which are asymptotically nonexpansive in the intermediate sense

    International Nuclear Information System (INIS)

    Chidume, C.E.; Shahzad, Naseer; Zegeye, Habtu

    2003-08-01

    Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T : K → E be a non-self mapping which is asymptotically nonexpansive in the intermediate sense with F(T) := {x is an element of K : Tx x} ≠ 0. A demiclosed principle for T is proved. Moreover, if T is completely continuous, an iterative sequence {x n } is constructed which converges strongly to some x* is an element of F(T). If T is not assumed to be completely continuous but the dual E* of E is assumed to have the Kadec-Klee property, then {x n } converges weakly to some x* is an element of F(T). The operator P which plays a central role in our proofs is, in this case, the Banach space analogue of the proximity map in Hilbert spaces. (author)

  16. A remark on smooth images of Banach spaces

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr Pavel; Johanis, M.

    2018-01-01

    Roč. 458, č. 2 (2018), s. 1307-1313 ISSN 0022-247X R&D Projects: GA ČR GA16-07378S Institutional support: RVO:67985840 Keywords : smooth surjections Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 http://www.sciencedirect.com/science/ article /pii/S0022247X17309186?via%3Dihub

  17. Fusion frames and G-frames in Banach spaces

    Indian Academy of Sciences (India)

    Author Affiliations. Amir Khosravi1 Behrooz Khosravi2. Faculty of Mathematical Sciences and Computer, Tarbiat Moallem University, 599 Ayatollah Taleghani Ave., Tehran 15618, Iran; Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), ...

  18. On Kurzweil-Stieltjes integral in a Banach space

    Czech Academy of Sciences Publication Activity Database

    Monteiro, G.A.; Tvrdý, Milan

    2012-01-01

    Roč. 137, č. 4 (2012), s. 365-381 ISSN 0862-7959 Institutional research plan: CEZ:AV0Z10190503 Institutional support: RVO:67985840 Keywords : Kurzweil-Stielthes integral * substitution formula * integration-by-parts Subject RIV: BA - General Mathematics http://www.dml.cz/handle/10338.dmlcz/142992

  19. Some remarks on smooth renormings of Banach spaces

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr Pavel; Russo, T.

    2017-01-01

    Roč. 455, č. 2 (2017), s. 1272-1284 ISSN 0022-247X R&D Projects: GA ČR GA16-07378S Institutional support: RVO:67985840 Keywords : Fréchet smooth * approximation of norms * Ck-smooth norm Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022247X17305462?via%3Dihub

  20. A remark on smooth images of Banach spaces

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr Pavel; Johanis, M.

    2018-01-01

    Roč. 458, č. 2 (2018), s. 1307-1313 ISSN 0022-247X R&D Projects: GA ČR GA16-07378S Institutional support: RVO:67985840 Keywords : smooth surjections Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022247X17309186?via%3Dihub

  1. Restricting uniformly open surjections

    Czech Academy of Sciences Publication Activity Database

    Kania, Tomasz; Rmoutil, M.

    2017-01-01

    Roč. 355, č. 9 (2017), s. 925-928 ISSN 1631-073X Institutional support: RVO:67985840 Keywords : Banach space * uniform spaces Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.396, year: 2016 http://www.sciencedirect.com/science/article/pii/S1631073X17302261?via%3Dihub

  2. A Note on a Semilinear Fractional Differential Equation of Neutral Type with Infinite Delay

    Directory of Open Access Journals (Sweden)

    Gisle M. Mophou

    2010-01-01

    Full Text Available We deal in this paper with the mild solution for the semilinear fractional differential equation of neutral type with infinite delay: Dαx(t+Ax(t=f(t,xt, t∈[0,T], x(t=ϕ(t, t∈]−∞,0], with T>0 and 0<α<1. We prove the existence (and uniqueness of solutions, assuming that −A is a linear closed operator which generates an analytic semigroup (T(tt≥0 on a Banach space 𝕏 by means of the Banach's fixed point theorem. This generalizes some recent results.

  3. Steepest descent approximations for accretive operator equations

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1993-03-01

    A necessary and sufficient condition is established for the strong convergence of the steepest descent approximation to a solution of equations involving quasi-accretive operators defined on a uniformly smooth Banach space. (author). 49 refs

  4. Dedekind σ-complete vector lattice of b-AM-compact operators ...

    African Journals Online (AJOL)

    We give several equivalent conditions characterizing the case when Krb-AM(E,F) is Dedekind σ-complete. Moreover, we describe the case when the space of all regular b-AM-compact operators from E to F is complete under the b-AM-norm. Keywords: Banach lattices, b-AM-compact operator, discrete space ...

  5. Asymptotically Stable Solutions of a Generalized Fractional Quadratic Functional-Integral Equation of Erdélyi-Kober Type

    Directory of Open Access Journals (Sweden)

    Mohamed Abdalla Darwish

    2014-01-01

    Full Text Available We study a generalized fractional quadratic functional-integral equation of Erdélyi-Kober type in the Banach space BC(ℝ+. We show that this equation has at least one asymptotically stable solution.

  6. Perturbation of Operators and Applications to Frame Theory

    DEFF Research Database (Denmark)

    Christensen, Ole; Casazza, P.

    1997-01-01

    A celebrated classical result states that an operator U on a Banach space is invertible if it is close enough to the identity operator I in the sense that ||I - U|| application we prove new theorems concerning...

  7. Differential structures in C*-algebras

    Indian Academy of Sciences (India)

    Second and higher order differential structure defined by a closed symmetric operator. Differential ... (1) General theory – differential seminorm approach and growth conditions ...... S is dual of a Banach space, and the weak ∗-topology on A2.

  8. Strong ergodic theorem for commutative semigroup of non ...

    Indian Academy of Sciences (India)

    M Azhini

    2017-08-14

    Aug 14, 2017 ... of non-Lipschitzian mappings in multi-Banach space ... to studying nonlinear ergodic theory for (asymptotically) non-expansive ... As we know, Bruck's lemmas are essential tools in the proof of almost all mean ergodic theorem ...

  9. Boundary controllability of integrodifferential systems in Banach ...

    Indian Academy of Sciences (India)

    solution to state space system, the control must be taken in a space of ... this paper is to study the boundary controllability of nonlinear integrodifferential systems ... be a linear closed and densely defined operator with Dً'ق E and let ( be a linear ... (iv) For all t 2 ً0; bٹ and u 2 U, TًtقBu 2 DًAق. ... The construction of the bounded.

  10. Existence of positive solutions for nonlocal second-order boundary value problem with variable parameter in Banach spaces

    Directory of Open Access Journals (Sweden)

    Zhang Peiguo

    2011-01-01

    Full Text Available Abstract By obtaining intervals of the parameter λ, this article investigates the existence of a positive solution for a class of nonlinear boundary value problems of second-order differential equations with integral boundary conditions in abstract spaces. The arguments are based upon a specially constructed cone and the fixed point theory in cone for a strict set contraction operator. MSC: 34B15; 34B16.

  11. Boundary Controllability of Nonlinear Fractional Integrodifferential Systems

    Directory of Open Access Journals (Sweden)

    Ahmed HamdyM

    2010-01-01

    Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.

  12. Appearance of eigen modes for the linearized Vlasov-Poisson equation

    International Nuclear Information System (INIS)

    Degond, P.

    1983-01-01

    In order to determine the asymptotic behaviour, when the time goes to infinity, of the solution of the linearized Vlasov-Poisson equation, we use eigen modes, associated to continuous linear functionals on a Banach space of analytic functions [fr

  13. Quaestiones Mathematicae - Vol 32, No 2 (2009)

    African Journals Online (AJOL)

    Into isomorphisms in tensor products of Banach spaces · EMAIL FULL TEXT EMAIL FULL TEXT · DOWNLOAD FULL TEXT DOWNLOAD FULL TEXT. Eve Oja, Vaiki Randala. http://dx.doi.org/10.2989/QM.2009.32.2.9.802 ...

  14. Strong convergence of modified Ishikawa iterations for nonlinear ...

    Indian Academy of Sciences (India)

    interval [0, 1]. The second iteration process is referred to as Ishikawa's iteration process [11] which is .... Let E be a smooth Banach space with dual E∗ ..... and applications, in: Theory and Applications of Nonlinear Operators of Accretive and.

  15. Khinchin's inequality, Dunford–Pettis and compact operators on the ...

    Indian Academy of Sciences (India)

    Department of Mathematics, University of Constanta, 8700 Constanta, Romania. E-mail: dpopa@univ-ovidius.ro. MS received 10 November 2005. Abstract. We prove that if X, Y are Banach spaces, a compact Hausdorff space and. U: C( ,X) → Y is a bounded linear operator, and if U is a Dunford–Pettis operator the range of ...

  16. Diliberto–Straus algorithm for the uniform approximation by a sum of ...

    Indian Academy of Sciences (India)

    AIDA KH ASGAROVA

    uniform approximation of a bivariate function, defined on a rectangle with ... Let U and V be subspaces of a Banach space having central proximity ..... that this idea can be useful in future attempts to prove the convergence of the Diliberto–.

  17. On prime and semiprime rings with generalized derivations and non ...

    Indian Academy of Sciences (India)

    that any continuous derivation on a commutative Banach algebra has the range in the .... isomorphic to a dense ring of linear transformations of some vector space r over P and .... This section deals with application of our main results. Here A ...

  18. On the Carleman classes of vectors of a scalar type spectral operator

    Directory of Open Access Journals (Sweden)

    Marat V. Markin

    2004-01-01

    Full Text Available The Carleman classes of a scalar type spectral operator in a reflexive Banach space are characterized in terms of the operator's resolution of the identity. A theorem of the Paley-Wiener type is considered as an application.

  19. A Conditional Fourier-Feynman Transform and Conditional Convolution Product with Change of Scales on a Function Space II

    Directory of Open Access Journals (Sweden)

    Dong Hyun Cho

    2017-01-01

    Full Text Available Using a simple formula for conditional expectations over continuous paths, we will evaluate conditional expectations which are types of analytic conditional Fourier-Feynman transforms and conditional convolution products of generalized cylinder functions and the functions in a Banach algebra which is the space of generalized Fourier transforms of the measures on the Borel class of L2[0,T]. We will then investigate their relationships. Particularly, we prove that the conditional transform of the conditional convolution product can be expressed by the product of the conditional transforms of each function. Finally we will establish change of scale formulas for the conditional transforms and the conditional convolution products. In these evaluation formulas and change of scale formulas, we use multivariate normal distributions so that the conditioning function does not contain present positions of the paths.

  20. Stationary theory of scattering

    International Nuclear Information System (INIS)

    Kato, T.

    1977-01-01

    A variant of the stationary methods is described, and it is shown that it is useful in a wide range of problems, including scattering, by long-range potentials, two-space scattering, and multichannel scattering. The method is based on the notion of spectral forms. The paper is restricted to the simplest case of continuous spectral forms defined on a Banach space embedded in the basic Hilbert space. (P.D.)

  1. Introduction

    Indian Academy of Sciences (India)

    Let X_1 denote the closed unit ball of X. Let X* denote the space of continuous linear functionals f on X, i.e linear scalar-valued maps on X such that, ||f||= the supremum of |f| over X_1, is finite . ||f|| in turn defines a norm on the vector space X*, which again becomes a Banach space. This is called the dual of X. An important ...

  2. Coverings, Networks and Weak Topologies

    Czech Academy of Sciences Publication Activity Database

    Dow, A.; Junnila, H.; Pelant, Jan

    2006-01-01

    Roč. 53, č. 2 (2006), s. 287-320 ISSN 0025-5793 R&D Projects: GA ČR GA201/97/0216 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach spaces * weak topologies * networks topologies Subject RIV: BA - General Mathematics

  3. Numerical Treatment of Fixed Point Applied to the Nonlinear Fredholm Integral Equation

    Directory of Open Access Journals (Sweden)

    Berenguer MI

    2009-01-01

    Full Text Available The authors present a method of numerical approximation of the fixed point of an operator, specifically the integral one associated with a nonlinear Fredholm integral equation, that uses strongly the properties of a classical Schauder basis in the Banach space .

  4. Boundary-value problems for first and second order functional differential inclusions

    Directory of Open Access Journals (Sweden)

    Shihuang Hong

    2003-03-01

    Full Text Available This paper presents sufficient conditions for the existence of solutions to boundary-value problems of first and second order multi-valued differential equations in Banach spaces. Our results obtained using fixed point theorems, and lead to new existence principles.

  5. For eagles only: probably the most difficult proof of the Arzela-Ascoli ...

    African Journals Online (AJOL)

    Let C(K) denote the Banach space of all (real or complex) continuous functions on a compact Hausdorff space K. We present a novel point of view on the classical Arzela-Ascoli theorem: For every pointwise bounded and equicontinuous subset F of C(K) there is a continuous mapping J :βF → C(K), where F denotes the ...

  6. Best Proximity Points of Contractive-type and Nonexpansive-type Mappings

    Directory of Open Access Journals (Sweden)

    R. Kavitha

    2018-02-01

    Full Text Available The purpose of this paper is to obtain best proximity point theorems for multivalued nonexpansive-type and contractive-type mappings on complete metric spaces and on certain closed convex subsets of Banach spaces. We obtain a convergence result under some assumptions and we prove the existence of common best proximity points for a sequence of multivalued contractive-type mappings.

  7. Maximal regularity for non-autonomous stochastic evolution ...

    Indian Academy of Sciences (India)

    Tôn Vi?t T?

    2017-11-17

    Nov 17, 2017 ... in a separable UMD Banach space E of type 2 with norm. ·. Here, W denotes a ... cases, e.g., the case where A is a bounded linear operator [3]. .... measurable if it is the pointwise limit of a sequence of simple functions. .... Here, Fβ,σ ((0, T]; E) denotes a weighted Hölder continuous function space introduced.

  8. STABILITY OF A FUNCTIONAL EQUATION IN COMPLEX BANACH SPACES

    Directory of Open Access Journals (Sweden)

    PRATAP MONDAL

    2016-12-01

    Full Text Available Using fixed point technique, in the present paper , we wish to examine gen- eralization of the Hyers-Ulam-Rassias stability theorem for the functional equations f ( 2 x + i y + f ( x + 2 i y = 4 f ( x + i y + f ( x + f ( y (0.1 and f ( 2 x + i y .

  9. On McShane integrability of Banach space-valued functions

    Czech Academy of Sciences Publication Activity Database

    Kurzweil, Jaroslav; Schwabik, Štefan

    2004-01-01

    Roč. 29, č. 2 (2004), s. 763-780 ISSN 0147-1937 R&D Projects: GA ČR GA201/01/1199 Institutional research plan: CEZ:AV0Z1019905 Keywords : McShane integral * vector integration Subject RIV: BA - General Mathematics

  10. Less than one implies zero

    NARCIS (Netherlands)

    Schwenninger, Felix L.; Zwart, Hans

    2015-01-01

    In this paper we show that from an estimate of the form supt≥0 C(t) - cos(at)I < 1, we can conclude that C(t) equals cos(at)I. Here (C(t)) t≥0 is a strongly continuous cosine family on a Banach space.

  11. Nonlinear approximation with dictionaries I. Direct estimates

    DEFF Research Database (Denmark)

    Gribonval, Rémi; Nielsen, Morten

    2004-01-01

    We study various approximation classes associated with m-term approximation by elements from a (possibly) redundant dictionary in a Banach space. The standard approximation class associated with the best m-term approximation is compared to new classes defined by considering m-term approximation w...

  12. Existence results for impulsive semilinear damped differential inclusions

    Directory of Open Access Journals (Sweden)

    Mouffak Benchohra

    2003-06-01

    Full Text Available In this paper we investigate the existence of mild solutions for first and second order impulsive semilinear evolution inclusions in separable Banach spaces. By using suitable fixed point theorems, we study the case when the multivalued map has convex and nonconvex values.

  13. Approximate source conditions for nonlinear ill-posed problems—chances and limitations

    International Nuclear Information System (INIS)

    Hein, Torsten; Hofmann, Bernd

    2009-01-01

    In the recent past the authors, with collaborators, have published convergence rate results for regularized solutions of linear ill-posed operator equations by avoiding the usual assumption that the solutions satisfy prescribed source conditions. Instead the degree of violation of such source conditions is expressed by distance functions d(R) depending on a radius R ≥ 0 which is an upper bound of the norm of source elements under consideration. If d(R) tends to zero as R → ∞ an appropriate balancing of occurring regularization error terms yields convergence rates results. This approach was called the method of approximate source conditions, originally developed in a Hilbert space setting. The goal of this paper is to formulate chances and limitations of an application of this method to nonlinear ill-posed problems in reflexive Banach spaces and to complement the field of low order convergence rates results in nonlinear regularization theory. In particular, we are going to establish convergence rates for a variant of Tikhonov regularization. To keep structural nonlinearity conditions simple, we update the concept of degree of nonlinearity in Hilbert spaces to a Bregman distance setting in Banach spaces

  14. On 0-Complete Partial Metric Spaces and Quantitative Fixed Point Techniques in Denotational Semantics

    Directory of Open Access Journals (Sweden)

    N. Shahzad

    2013-01-01

    Full Text Available In 1994, Matthews introduced the notion of partial metric space with the aim of providing a quantitative mathematical model suitable for program verification. Concretely, Matthews proved a partial metric version of the celebrated Banach fixed point theorem which has become an appropriate quantitative fixed point technique to capture the meaning of recursive denotational specifications in programming languages. In this paper we show that a few assumptions in statement of Matthews fixed point theorem can be relaxed in order to provide a quantitative fixed point technique useful to analyze the meaning of the aforementioned recursive denotational specifications in programming languages. In particular, we prove a new fixed point theorem for self-mappings between partial metric spaces in which the completeness has been replaced by 0-completeness and the contractive condition has been weakened in such a way that the new one best fits the requirements of practical problems in denotational semantics. Moreover, we provide examples that show that the hypothesis in the statement of our new result cannot be weakened. Finally, we show the potential applicability of the developed theory by means of analyzing a few concrete recursive denotational specifications, some of them admitting a unique meaning and others supporting multiple ones.

  15. Perturbation of Operators and Applications to Frame Theory

    DEFF Research Database (Denmark)

    Christensen, Ole; Casazza, P.

    1996-01-01

    A celebrated classical result states that an operator Uon a Banach space is invertible, if it is close enough to the identityoperator I. Here we showthat U actually is invertible under a much weaker condition. As anapplication we prove new theorems concerning stability of frames (andframe...

  16. Proceedings – Mathematical Sciences | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    In this paper, we study the matrix multiplication operators on Banach function spaces and discuss their applications in semigroups for solving the abstract Cauchy problem. Author Affiliations. H Hudzik1 Rajeev Kumar2 Romesh Kumar2. Faculty of Mathematics and Computer Science, Adam Mickiewicz University ...

  17. Existence of Positive Solutions for a Coupled System of (p, q-Laplacian Fractional Higher Order Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    K.R. Prasad

    2015-11-01

    Full Text Available In this paper, we establish the existence of at least three positive solutions for a system of (p,q-Laplacian fractional order two-point boundary value problems by applying five functionals fixed point theorem under suitable conditions on a cone in a Banach space.

  18. A New Result Concerning the Solvability of a Class of General Systems of Variational Equations with Nonmonotone Operators: Applications to Dirichlet and Neumann Nonlinear Problems

    Directory of Open Access Journals (Sweden)

    Luisa Toscano

    2016-01-01

    Full Text Available A new result of solvability for a wide class of systems of variational equations depending on parameters and governed by nonmonotone operators is found in a Banach real and reflexive space with applications to Dirichlet and Neumann problems related to nonlinear elliptic systems.

  19. On the problem of the existence of the solutions of the nonlinear nonsingular equations of quantum field theory

    International Nuclear Information System (INIS)

    Nelipa, N.F.

    1978-01-01

    The existence of the solution of the nonlinear, singular equations of quantum field theory is discussed. By making use of the Banach's and Schauder's fixed point theorems, the condition of the existence of these equations is found. As some illustration, these methods were applied to the equations for the π-scattering on static nucleon. The investigations of the other equations of quantum field theory (Chew-Low, double dispersin relation, Green's function) lead to the similar result. The application of the Newton-Kantorovich method to the Chew-Low equations also gives the similar result. What are the causes of such situation[ The main suggestions which the author has used were that the Banach's, the Schauder's, and the Newton-Kantorovich methods were applied and the Hoelder space was choosen. It may be that the method are crude. It may be that the solutions do not belong to the Hoelder space. Now it is rather difficult to say which role each of these two suggestions plays. (Kobatake, H.)

  20. Simultaneous triangularization

    CERN Document Server

    Radjavi, Heydar

    2000-01-01

    A collection of matrices is said to be triangularizable if there is an invertible matrix S such that S1 AS is upper triangular for every A in the collection. This generalization of commutativity is the subject of many classical theorems due to Engel, Kolchin, Kaplansky, McCoy and others. The concept has been extended to collections of bounded linear operators on Banach spaces: such a collection is defined to be triangularizable if there is a maximal chain of subspaces of the Banach space, each of which is invariant under every member of the collection. Most of the classical results have been generalized to compact operators, and there are also recent theorems in the finite-dimensional case. This book is the first comprehensive treatment of triangularizability in both the finite and infinite-dimensional cases. It contains numerous very recent results and new proofs of many of the classical theorems. It provides a thorough background for research in both the linear-algebraic and operator-theoretic aspects of tr...

  1. Invariant boxes and stability of some systems from biomathematics and chemical reactions

    International Nuclear Information System (INIS)

    Pavel, N.H.

    1984-08-01

    A general theorem on the flow-invariance of a time-dependent rectangular box with respect to a differential system is first recalled [''Analysis of some non-linear problems'' in Banach Spaces and Applications, Univ. of Iasi (Romania) (1982)]. Then a theorem applicable to the study of some differential systems from biomathematics and chemical reactions is given and proved. The theorem can be applied to enzymatic reactions, the chemical mechanism in the Belousov reaction, and the kinetic system for the chemical scheme of Hanusse of two processes with three intermediate species [in Pavel, N.H., Differential Equations, Flow-invariance and Applications, Pitman Publishing, Ltd., London (to appear)]. Next, the matrices A for which the corresponding linear system x'=Ax is component-wise positive asymptotically stable are characterized. In the Appendix a partial answer to an open problem regarding the preservation of both continuity and dissipativity in the extension of functions to a Banach space is given

  2. Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator

    Science.gov (United States)

    Bogdan, V. M.; Bond, V. B.

    1980-01-01

    The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

  3. Global optimization of cyclic Kannan nonexpansive mappings in ...

    African Journals Online (AJOL)

    As an application of the existence theorem, we conclude an old fixed point problem in Banach spaces which are not reflexive necessarily. Examples are given to support the usability of our main conclusions. Keywords: Best proximity point, fixed point, cyclic Kannan nonexpansive mapping, T-uniformly semi-normal structure, ...

  4. Some aspects of non-linear semi-groups

    International Nuclear Information System (INIS)

    Plant, A.T.

    1976-01-01

    Some simpler theorems in the theory of non-linear semi-groups of non-reflexive Banach spaces are proved, with the intention to introduce the reader to this active field of research. Flow invariance, in particular for Lipschitz generators, and contraction semi-groups are discussed in some detail. (author)

  5. Existence principles for inclusions of Hammerstein type involving noncompact acyclic multivalued maps

    Directory of Open Access Journals (Sweden)

    Jean-Francois Couchouron

    2002-01-01

    Full Text Available We apply Monch type fixed point theorems for acyclic multivalued maps to the solvability of inclusions of Hammerstein type in Banach spaces. Our approach makes possible to unify and improve the existence theories for nonlinear evolution problems and abstract integral inclusions of Volterra and Fredholm type.

  6. On the Moduli of Convexity

    Czech Academy of Sciences Publication Activity Database

    Guirao, A. J.; Hájek, Petr Pavel

    2007-01-01

    Roč. 135, č. 10 (2007), s. 3233-3240 ISSN 0002-9939 R&D Projects: GA AV ČR IAA100190502 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach spaces * moduli of convexity * uniformly rotund norms Subject RIV: BA - General Mathematics Impact factor: 0.520, year: 2007

  7. Subordination principle for fractional evolution equations

    NARCIS (Netherlands)

    Bazhlekova, E.G.

    2000-01-01

    The abstract Cauchy problem for the fractional evolution equation Daa = Au, a > 0, (1) where A is a closed densely de??ned operator in a Banach space, is investigated. The subordination principle, presented earlier in [J. P r ??u s s, Evolutionary In- tegral Equations and Applications. Birkh??auser,

  8. On Functional Calculus Estimates

    NARCIS (Netherlands)

    Schwenninger, F.L.

    2015-01-01

    This thesis presents various results within the field of operator theory that are formulated in estimates for functional calculi. Functional calculus is the general concept of defining operators of the form $f(A)$, where f is a function and $A$ is an operator, typically on a Banach space. Norm

  9. Existence of Mild Solutions for Impulsive Fractional Integro-Differential Inclusions with State-Dependent Delay

    Directory of Open Access Journals (Sweden)

    Selvaraj Suganya

    2017-01-01

    Full Text Available In this manuscript, we implement Bohnenblust–Karlin’s fixed point theorem to demonstrate the existence of mild solutions for a class of impulsive fractional integro-differential inclusions (IFIDI with state-dependent delay (SDD in Banach spaces. An example is provided to illustrate the obtained abstract results.

  10. Li-Yorke chaos in linear dynamics

    Czech Academy of Sciences Publication Activity Database

    Bernardes Jr., N.C.; Bonilla, A.; Müller, Vladimír; Peris, A.

    2015-01-01

    Roč. 35, č. 6 (2015), s. 1723-1745 ISSN 0143-3857 R&D Projects: GA ČR GA201/09/0473; GA AV ČR IAA100190903 Institutional support: RVO:67985840 Keywords : Li-York chaos * Banach space * Fréchet space Subject RIV: BA - General Mathematics Impact factor: 0.983, year: 2015 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9884748&fileId=S0143385714000200

  11. Summing Boolean Algebras

    Institute of Scientific and Technical Information of China (English)

    Antonio AIZPURU; Antonio GUTI(E)RREZ-D(A)VILA

    2004-01-01

    In this paper we will study some families and subalgebras ( ) of ( )(N) that let us characterize the unconditional convergence of series through the weak convergence of subseries ∑i∈A xi, A ∈ ( ).As a consequence, we obtain a new version of the Orlicz-Pettis theorem, for Banach spaces. We also study some relationships between algebraic properties of Boolean algebras and topological properties of the corresponding Stone spaces.

  12. Existence of solutions for nonlinear mixed type integrodifferential equation of second order

    Directory of Open Access Journals (Sweden)

    Haribhau Laxman Tidke

    2010-04-01

    Full Text Available In this paper, we investigate the existence of solutions for nonlinear mixed Volterra-Fredholm integrodifferential equation of second order with nonlocal conditions in Banach spaces. Our analysis is based on Leray-Schauder alternative, rely on a priori bounds of solutions and the inequality established by B. G. Pachpatte.

  13. Structures of generalized 3-circular projections for symmetric norms

    Indian Academy of Sciences (India)

    Generalized bi-circular projection has been studied by many authors (see the subse- quent paragraph and references at the end of this paper). In particular, Botelho [4] and. Botelho and Jamison [5–8] extensively investigated the structures of GBPs for different. Banach spaces whose isometry group has concrete description ...

  14. A limit set trichotomy for order-preserving systems on time scales

    Directory of Open Access Journals (Sweden)

    Christian Poetzsche

    2004-04-01

    Full Text Available In this paper we derive a limit set trichotomy for abstract order-preserving 2-parameter semiflows in normal cones of strongly ordered Banach spaces. Additionally, to provide an example, Muller's theorem is generalized to dynamic equations on arbitrary time scales and applied to a model from population dynamics.

  15. Maximal Regularity of the Discrete Harmonic Oscillator Equation

    Directory of Open Access Journals (Sweden)

    Airton Castro

    2009-01-01

    Full Text Available We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterization of lp-maximal regularity—or well posedness—solely in terms of R-boundedness properties of the resolvent operator involved in the equation.

  16. On Nonlinear Neutral Fractional Integrodifferential Inclusions with Infinite Delay

    Directory of Open Access Journals (Sweden)

    Fang Li

    2012-01-01

    Full Text Available Of concern is a class of nonlinear neutral fractional integrodifferential inclusions with infinite delay in Banach spaces. A theorem about the existence of mild solutions to the fractional integrodifferential inclusions is obtained based on Martelli’s fixed point theorem. An example is given to illustrate the existence result.

  17. Existence of solutions of abstract fractional impulsive semilinear evolution equations

    Directory of Open Access Journals (Sweden)

    K. Balachandran

    2010-01-01

    Full Text Available In this paper we prove the existence of solutions of fractional impulsive semilinear evolution equations in Banach spaces. A nonlocal Cauchy problem is discussed for the evolution equations. The results are obtained using fractional calculus and fixed point theorems. An example is provided to illustrate the theory.

  18. Asymptotic behaviour of firmly non expansive sequences

    International Nuclear Information System (INIS)

    Rouhani, B.D.

    1993-04-01

    We introduce the notion of firmly non expansive sequences in a Banach space and present several results concerning their asymptotic behaviour extending previous results and giving an affirmative answer to an open question raised by S. Reich and I. Shafir. Applications to averaged mappings are also given. (author). 16 refs

  19. Functional analysis

    CERN Document Server

    Bachman, George

    1998-01-01

    Excellent treatment of the subject geared toward students with background in linear algebra, advanced calculus, physics and engineering. Text covers introduction to inner-product spaces, normed and metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach theorem and its consequences, spectral notions, square roots, a spectral decomposition theorem, and many other related subjects. Chapters conclude with exercises intended to test and reinforce reader's understanding of text material. A glossary of definitions, detailed proofs of theorems, bibliography, and index of sym

  20. Stability of a Jensen Type Logarithmic Functional Equation on Restricted Domains and Its Asymptotic Behaviors

    Directory of Open Access Journals (Sweden)

    Chung Jae-Young

    2010-01-01

    Full Text Available Let be the set of positive real numbers, a Banach space, and , with . We prove the Hyers-Ulam stability of the Jensen type logarithmic functional inequality in restricted domains of the form for fixed with or and . As consequences of the results we obtain asymptotic behaviors of the inequality as .

  1. Covariant Transform

    OpenAIRE

    Kisil, Vladimir V.

    2010-01-01

    The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable or vacuum vectors which are not admissible. Covariant transform extends an applicability of the popular wavelets construction to classic examples like the Hardy space H_2, Banach spaces, covariant functional calculus and many others. Keywords: Wavelets, cohe...

  2. 24th International Workshop in Operator Theory and its Applications

    CERN Document Server

    Dritschel, Michael

    2015-01-01

    This volume gathers contributions from the International Workshop on Operator Theory and Its Applications (IWOTA) held in Bangalore, India, in December 2013. All articles were written by experts and cover a broad range of original material at the cutting edge of operator theory and its applications. Topics include multivariable operator theory, operator theory on indefinite metric spaces (Krein and Pontryagin spaces) and its applications, spectral theory with applications to differential operators, the geometry of Banach spaces, scattering and time varying linear systems, and wavelets and coherent states.

  3. On an nth-order infinitesimal generator and time-dependent operator differential equation with a strongly almost periodic solution

    Directory of Open Access Journals (Sweden)

    Aribindi Satyanarayan Rao

    2002-01-01

    Full Text Available In a Banach space, if u is a Stepanov almost periodic solution of a certain nth-order infinitesimal generator and time-dependent operator differential equation with a Stepanov almost periodic forcing function, then u,u′,…,u (n−2 are all strongly almost periodic and u (n−1 is weakly almost periodic.

  4. On coarse embeddings into c0(Γ)

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr Pavel; Schlumprecht, T.

    2018-01-01

    Roč. 69, č. 1 (2018), s. 211-222 ISSN 0033-5606 R&D Projects: GA ČR GA16-07378S Institutional support: RVO:67985840 Keywords : Banach space Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.602, year: 2016 https://academic.oup.com/qjmath/ article /69/1/211/4080339

  5. On coarse embeddings into c0(Γ)

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr Pavel; Schlumprecht, T.

    2018-01-01

    Roč. 69, č. 1 (2018), s. 211-222 ISSN 0033-5606 R&D Projects: GA ČR GA16-07378S Institutional support: RVO:67985840 Keywords : Banach space Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.602, year: 2016 https://academic.oup.com/qjmath/article/69/1/211/4080339

  6. polynomially peripheral range-preserving maps between Banach ...

    Indian Academy of Sciences (India)

    11

    Tg) = σA(f.g), for all f and g in A, is a weighted composition operator, where ... case where c = ab and they characterize the general form of a surjection T ... dorff spaces X and Y, respectively, and show that if S is a norm-preserving map ... peaking function with P(g) = {z ∈ X : f(z) = f(x)} ⊆ Mf , so each maximum set contains.

  7. Feynman's Operational Calculi: Spectral Theory for Noncommuting Self-adjoint Operators

    International Nuclear Information System (INIS)

    Jefferies, Brian; Johnson, Gerald W.; Nielsen, Lance

    2007-01-01

    The spectral theorem for commuting self-adjoint operators along with the associated functional (or operational) calculus is among the most useful and beautiful results of analysis. It is well known that forming a functional calculus for noncommuting self-adjoint operators is far more problematic. The central result of this paper establishes a rich functional calculus for any finite number of noncommuting (i.e. not necessarily commuting) bounded, self-adjoint operators A 1 ,..., A n and associated continuous Borel probability measures μ 1 , ?, μ n on [0,1]. Fix A 1 ,..., A n . Then each choice of an n-tuple (μ 1 ,...,μ n ) of measures determines one of Feynman's operational calculi acting on a certain Banach algebra of analytic functions even when A 1 , ..., A n are just bounded linear operators on a Banach space. The Hilbert space setting along with self-adjointness allows us to extend the operational calculi well beyond the analytic functions. Using results and ideas drawn largely from the proof of our main theorem, we also establish a family of Trotter product type formulas suitable for Feynman's operational calculi

  8. A new iteration process for generalized lipschitz pseudo-contractive and generalized lipschitz accretive mappings

    International Nuclear Information System (INIS)

    Chidume, C.E.; Ofoedu, E.U.

    2007-07-01

    Let K be a nonempty closed convex subset of a real Banach space E. Let T : K → K be a generalized Lipschitz pseudo-contractive mapping such that F(T) := { x element of K : Tx = x} ≠ 0. Let { α n } n ≥ 1 , { λ n } n ≥ 1 and { θ n } n ≥ 1 be real sequences in (0, 1) such that α n = o( θ n ), lim n →∞ λ n = 0 and λ n ( α n + θ n ) 1 element of K, let the sequence { x n } n ≥ 1 be iteratively generated by x n+1 = (1 - λ n α n )x n + λ n α n Tx n - λ n θ n (x n - x 1 ), n ≥ 1. Then, { x n } n ≥ 1 is bounded. Moreover, if E is a reflexive Banach space with uniformly Gateaux differentiable norm and if Σ n=1 ∞ λ n θ n = ∞ is additionally assumed, then, under mild conditions, left brace# x n } n ≥ 1 converges strongly to some x* element of F(T). (author)

  9. On regular riesz operators | Raubenheimer | Quaestiones ...

    African Journals Online (AJOL)

    The r-asymptotically quasi finite rank operators on Banach lattices are examples of regular Riesz operators. We characterise Riesz elements in a subalgebra of a Banach algebra in terms of Riesz elements in the Banach algebra. This enables us to characterise r-asymptotically quasi finite rank operators in terms of adjoint ...

  10. Equivalence properties for the Radon-Nikodym property types and ...

    African Journals Online (AJOL)

    We show that the types I- and II-Λ-Radon-Nikodym Property of Banach spaces on the one hand, and the I- and II-Λ-Complete Continuity Property on the other, are equivalent properties whenever Λ is an ordering subset of a discrete abelian group. Mathematics Subject Classification (2000): Primary 46E40, 46G10; ...

  11. Prederivatives of gamma paraconvex set-valued maps and Pareto optimality conditions for set optimization problems.

    Science.gov (United States)

    Huang, Hui; Ning, Jixian

    2017-01-01

    Prederivatives play an important role in the research of set optimization problems. First, we establish several existence theorems of prederivatives for γ -paraconvex set-valued mappings in Banach spaces with [Formula: see text]. Then, in terms of prederivatives, we establish both necessary and sufficient conditions for the existence of Pareto minimal solution of set optimization problems.

  12. Perturbations of normally solvable nonlinear operators, I

    Directory of Open Access Journals (Sweden)

    William O. Ray

    1985-01-01

    Full Text Available Let X and Y be Banach spaces and let ℱ and be Gateaux differentiable mappings from X to Y In this note we study when the operator ℱ+ is surjective for sufficiently small perturbations of a surjective operator ℱ The methods extend previous results in the area of normal solvability for nonlinear operators.

  13. The fundamental solutions for fractional evolution equations of parabolic type

    Directory of Open Access Journals (Sweden)

    Mahmoud M. El-Borai

    2004-01-01

    Full Text Available The fundamental solutions for linear fractional evolution equations are obtained. The coefficients of these equations are a family of linear closed operators in the Banach space. Also, the continuous dependence of solutions on the initial conditions is studied. A mixed problem of general parabolic partial differential equations with fractional order is given as an application.

  14. Biorthogonal Systems Approximating the Solution of the Nonlinear Volterra Integro-Differential Equation

    Directory of Open Access Journals (Sweden)

    Berenguer MI

    2010-01-01

    Full Text Available This paper deals with obtaining a numerical method in order to approximate the solution of the nonlinear Volterra integro-differential equation. We define, following a fixed-point approach, a sequence of functions which approximate the solution of this type of equation, due to some properties of certain biorthogonal systems for the Banach spaces and .

  15. Distortion of Lipschitz functions on $c_0(Gamma)$

    Czech Academy of Sciences Publication Activity Database

    Hájek, Petr Pavel; Novotný, M.

    2018-01-01

    Roč. 146, č. 5 (2018), s. 2173-2180 ISSN 0002-9939 R&D Projects: GA ČR GA16-07378S Institutional support: RVO:67985840 Keywords : Banach spaces Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.679, year: 2016 http://www.ams.org/journals/proc/2018-146-05/S0002-9939-2018-13945-3/

  16. Examples of the Application of Nonparametric Information Geometry to Statistical Physics

    Directory of Open Access Journals (Sweden)

    Giovanni Pistone

    2013-09-01

    Full Text Available We review a nonparametric version of Amari’s information geometry in which the set of positive probability densities on a given sample space is endowed with an atlas of charts to form a differentiable manifold modeled on Orlicz Banach spaces. This nonparametric setting is used to discuss the setting of typical problems in machine learning and statistical physics, such as black-box optimization, Kullback-Leibler divergence, Boltzmann-Gibbs entropy and the Boltzmann equation.

  17. Push-outs of derivations

    DEFF Research Database (Denmark)

    Grønbæk, Niels

    2008-01-01

    Let A be a Banach algebra and let X be a Banach A-bimodule. In studying H¹(A,X) it is often useful to extend a given derivation D: A->X to a Banach algebra B containing A as an ideal, thereby exploiting (or establishing) hereditary properties. This is usually done using (bounded/unbounded) approx...

  18. Controllability Problem of Fractional Neutral Systems: A Survey

    Directory of Open Access Journals (Sweden)

    Artur Babiarz

    2017-01-01

    Full Text Available The following article presents recent results of controllability problem of dynamical systems in infinite-dimensional space. Generally speaking, we describe selected controllability problems of fractional order systems, including approximate controllability of fractional impulsive partial neutral integrodifferential inclusions with infinite delay in Hilbert spaces, controllability of nonlinear neutral fractional impulsive differential inclusions in Banach space, controllability for a class of fractional neutral integrodifferential equations with unbounded delay, controllability of neutral fractional functional equations with impulses and infinite delay, and controllability for a class of fractional order neutral evolution control systems.

  19. Smooth Frechet subalgebras of C∗-algebras defined by first order ...

    Indian Academy of Sciences (India)

    which is a Banach ∗-algebra with a norm · such that x∗. = x, xy ≤ x y .... decomposition when one passes from Banach to Frechet case. ... A as an inverse limit of a sequence of Banach ∗-algebras as follows. Let the .... -subalgebra of U. The last inequality follows thus. Since ..... (3) Nachbin's weighted function algebras.

  20. Applications of functional analysis to optimal control problems

    International Nuclear Information System (INIS)

    Mizukami, K.

    1976-01-01

    Some basic concepts in functional analysis, a general norm, the Hoelder inequality, functionals and the Hahn-Banach theorem are described; a mathematical formulation of two optimal control problems is introduced by the method of functional analysis. The problem of time-optimal control systems with both norm constraints on control inputs and on state variables at discrete intermediate times is formulated as an L-problem in the theory of moments. The simplex method is used for solving a non-linear minimizing problem inherent in the functional analysis solution to this problem. Numerical results are presented for a train operation. The second problem is that of optimal control of discrete linear systems with quadratic cost functionals. The problem is concerned with the case of unconstrained control and fixed endpoints. This problem is formulated in terms of norms of functionals on suitable Banach spaces. (author)

  1. Renorming c0 and closed, bounded, convex sets with fixed point property for affine nonexpansive mappings

    Science.gov (United States)

    Nezir, Veysel; Mustafa, Nizami

    2017-04-01

    In 2008, P.K. Lin provided the first example of a nonreflexive space that can be renormed to have fixed point property for nonexpansive mappings. This space was the Banach space of absolutely summable sequences l1 and researchers aim to generalize this to c0, Banach space of null sequences. Before P.K. Lin's intriguing result, in 1979, Goebel and Kuczumow showed that there is a large class of non-weak* compact closed, bounded, convex subsets of l1 with fixed point property for nonexpansive mappings. Then, P.K. Lin inspired by Goebel and Kuczumow's ideas to give his result. Similarly to P.K. Lin's study, Hernández-Linares worked on L1 and in his Ph.D. thesis, supervisored under Maria Japón, showed that L1 can be renormed to have fixed point property for affine nonexpansive mappings. Then, related questions for c0 have been considered by researchers. Recently, Nezir constructed several equivalent norms on c0 and showed that there are non-weakly compact closed, bounded, convex subsets of c0 with fixed point property for affine nonexpansive mappings. In this study, we construct a family of equivalent norms containing those developed by Nezir as well and show that there exists a large class of non-weakly compact closed, bounded, convex subsets of c0 with fixed point property for affine nonexpansive mappings.

  2. Applied functional analysis

    CERN Document Server

    Griffel, DH

    2002-01-01

    A stimulating introductory text, this volume examines many important applications of functional analysis to mechanics, fluid mechanics, diffusive growth, and approximation. Detailed enough to impart a thorough understanding, the text is also sufficiently straightforward for those unfamiliar with abstract analysis. Its four-part treatment begins with distribution theory and discussions of Green's functions. Essentially independent of the preceding material, the second and third parts deal with Banach spaces, Hilbert space, spectral theory, and variational techniques. The final part outlines the

  3. Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings

    Directory of Open Access Journals (Sweden)

    Watcharaporn Cholamjiak

    2009-01-01

    Full Text Available We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006 and Nakajo and Takahashi (2003.

  4. Stability of abstract nonlinear nonautonomous differential-delay equations with unbounded history-responsive operators

    Science.gov (United States)

    Gil', M. I.

    2005-08-01

    We consider a class of nonautonomous functional-differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input-output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators.

  5. Ranges of operators and derivatives

    Czech Academy of Sciences Publication Activity Database

    Guirao, A. J.; Hájek, Petr Pavel; Montesinos, V.

    2010-01-01

    Roč. 367, č. 1 (2010), s. 29-33 ISSN 0022-247X R&D Projects: GA AV ČR IAA100190502; GA AV ČR IAA100190801 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach-space * smooth Subject RIV: BA - General Mathematics Impact factor: 1.174, year: 2010 http://www.sciencedirect.com/science/article/pii/S0022247X09010051

  6. Tensor product of left n-invertible operators

    Czech Academy of Sciences Publication Activity Database

    Duggal, B.P.; Müller, Vladimír

    2013-01-01

    Roč. 215, č. 2 (2013), s. 113-125 ISSN 0039-3223 R&D Projects: GA ČR GA201/09/0473 Institutional support: RVO:67985840 Keywords : Banach space * essentially left n- invertible operator * left n-invertible operator Subject RIV: BA - General Mathematics Impact factor: 0.630, year: 2013 http://journals.impan.pl/cgi-bin/doi?sm215-2-2

  7. Linear measure functional differential equations with infinite delay

    OpenAIRE

    Monteiro, G. (Giselle Antunes); Slavík, A.

    2014-01-01

    We use the theory of generalized linear ordinary differential equations in Banach spaces to study linear measure functional differential equations with infinite delay. We obtain new results concerning the existence, uniqueness, and continuous dependence of solutions. Even for equations with a finite delay, our results are stronger than the existing ones. Finally, we present an application to functional differential equations with impulses.

  8. Inverse operator of the generator of a C0-semigroup

    NARCIS (Netherlands)

    Gomilko, A.M.; Zwart, Heiko J.; Tomilov, Y

    2007-01-01

    Let $A$ be the generator of a uniformly bounded $C_0$-semigroup in a Banach space $X$ such that $A$ has a trivial kernel and a dense range. The question whether $A^{-1}$ is a generator of a $C_0$-semigroup is considered. It is shown that the answer is negative in general for $X = \\ell_p$, $p \\in (1,

  9. Some fixed point theorems on non-convex sets

    Directory of Open Access Journals (Sweden)

    Mohanasundaram Radhakrishnan

    2017-10-01

    Full Text Available In this paper, we prove that if $K$ is a nonempty weakly compact set in a Banach space $X$, $T:K\\to K$ is a nonexpansive map satisfying $\\frac{x+Tx}{2}\\in K$ for all $x\\in K$ and if $X$ is $3-$uniformly convex or $X$ has the Opial property, then $T$ has a fixed point in $K.$

  10. The basic properties of Bloch functions

    Directory of Open Access Journals (Sweden)

    Joseph A. Cima

    1979-01-01

    Full Text Available A Bloch function f(z is an analytic function on the unit disc whose derivative grows no faster than a constant times the reciprocal of the distance from z to ∂. We reprove here the basic analytic facts concerning Bloch functions. We establish the Banach space structure and collect facts concerning the geometry of the space. We indicate duality relationships, and known isomorphic correspondences are given. We give a rather complete list of references for further study in the case of several variables.

  11. The one-sided Ap conditions and local maximal operator

    Czech Academy of Sciences Publication Activity Database

    Bernardis, A.L.; Gogatishvili, Amiran; Martin-Reyes, F. J.; Ortega Salvador, P.; Pick, L.

    Roč. 55, č. 1 ( 2012 ), s. 79-104 ISSN 0013-0915 R&D Projects: GA ČR GA201/08/0383; GA ČR GA201/05/2033 Institutional research plan: CEZ:AV0Z10190503 Keywords : one-sided Ap conditions * one-sided local maximal operator * quasi-Banach function spaces * variable-exponent Lebesgue spaces Subject RIV: BA - General Mathematics Impact factor: 0.561, year: 2012 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8477114&fulltextType=RA&fileId=S0013091510000635

  12. Multidimensional singular integrals and integral equations

    CERN Document Server

    Mikhlin, Solomon Grigorievich; Stark, M; Ulam, S

    1965-01-01

    Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals

  13. On characterizations of quasi-metric completeness

    Energy Technology Data Exchange (ETDEWEB)

    Dag, H.; Romaguera, S.; Tirado, P.

    2017-07-01

    Hu proved in [4] that a metric space (X, d) is complete if and only if for any closed subspace C of (X, d), every Banach contraction on C has fixed point. Since then several authors have investigated the problem of characterizing the metric completeness by means of fixed point theorems. Recently this problem has been studied in the more general context of quasi-metric spaces for different notions of completeness. Here we present a characterization of a kind of completeness for quasi-metric spaces by means of a quasi-metric versions of Hu’s theorem. (Author)

  14. Existence of pseudo almost periodic solutions for a class of partial functional differential equations

    Directory of Open Access Journals (Sweden)

    Hui-Sheng Ding

    2013-04-01

    Full Text Available In this paper, we first introduce a new class of pseudo almost periodic type functions and investigate some properties of pseudo almost periodic type functions; and then we discuss the existence of pseudo almost periodic solutions to the class of abstract partial functional differential equations $x'(t=Ax(t+f(t,x_t$ with finite delay in a Banach space X.

  15. An introduction to geometric theory of fully nonlinear parabolic equations

    International Nuclear Information System (INIS)

    Lunardi, A.

    1991-01-01

    We study a class of nonlinear evolution equations in general Banach space being an abstract version of fully nonlinear parabolic equations. In addition to results of existence, uniqueness and continuous dependence on the data, we give some qualitative results about stability of the stationary solutions, existence and stability of the periodic orbits. We apply such results to some parabolic problems arising from combustion theory. (author). 24 refs

  16. Common fixed points for weakly compatible maps

    Indian Academy of Sciences (India)

    Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45

    In 1976, Jungck [4] proved a common fixed point theorem for commuting maps generalizing the Banach's fixed point theorem, which states that, 'let (X, d) be a complete metric space. If T satisfies d(Tx,Ty) ≤ kd(x,y) for each x,y ∈ X where 0 ≤ k < 1, then T has a unique fixed point in X'. This theorem has many applications, ...

  17. A quantitative version of Krein´s Theorem. To the memory of Vlastimil Pták

    Czech Academy of Sciences Publication Activity Database

    Fabian, Marián; Hájek, Petr Pavel; Montesinos, V.; Zizler, Václav

    2005-01-01

    Roč. 21, č. 1 (2005), s. 237-248 ISSN 0213-2230 R&D Projects: GA AV ČR(CZ) IAA1019003; GA ČR(CZ) GA201/01/1198; GA AV ČR(CZ) IAA1019205 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach spaces * weak compatness * Krein´s Theorem Subject RIV: BA - General Mathematics Impact factor: 0.855, year: 2005

  18. Existence of mild solutions of a semilinear evolution differential inclusions with nonlocal conditions

    Directory of Open Access Journals (Sweden)

    Reem A. Al-Omair

    2009-03-01

    Full Text Available In this paper we prove the existence of a mild solution for a semilinear evolution differential inclusion with nonlocal condition and governed by a family of linear operators, not necessarily bounded or closed, in a Banach space. No compactness assumption is assumed on the evolution operator generated by the family operators. Also, we prove that the set of mild solutions is compact.

  19. Ulam stability for fractional differential equations in the sense of Caputo operator

    Directory of Open Access Journals (Sweden)

    Rabha W. Ibrahim

    2012-12-01

    Full Text Available In this paper, we consider the Hyers-Ulam stability for the following fractional differential equations, in the sense ofcomplex Caputo fractional derivative defined, in the unit disk: cDßzf(z=G(f(z, cDázf(z,zf‘(z;z 0<á<1<ß<2 . Furthermore,a generalization of the admissible functions in complex Banach spaces is imposed and applications are illustrated.

  20. Existence and controllability results for damped second order impulsive functional differential systems with state-dependent delay

    Directory of Open Access Journals (Sweden)

    M. Mallika Arjunan

    2014-01-01

    Full Text Available In this paper, we investigate the existence and controllability of mild solutions for a damped second order impulsive functional differential equation with state-dependent delay in Banach spaces. The results are obtained by using Sadovskii's fixed point theorem combined with the theories of a strongly continuous cosine family of bounded linear operators. Finally, an example is provided to illustrate the main results.

  1. On The Integral Representation of Strictly Continuous Set-Valued Maps

    Directory of Open Access Journals (Sweden)

    Anaté K. Lakmon

    2015-11-01

    Full Text Available Let T be a completely regular topological space and C(T be the space of bounded, continuous real-valued functions on T. C(T is endowed with the strict topology (the topology generated by seminorms determined by continuous functions vanishing at in_nity. R. Giles ([13], p. 472, Theorem 4.6 proved in 1971 that the dual of C(T can be identi_ed with the space of regular Borel measures on T. We prove this result for positive, additive set-valued maps with values in the space of convex weakly compact non-empty subsets of a Banach space and we deduce from this result the theorem of R. Giles ([13], theorem 4.6, p.473.

  2. On the existence of dyons and dyonic black holes in Einstein–Yang–Mills theory

    International Nuclear Information System (INIS)

    Nolan, Brien C; Winstanley, Elizabeth

    2012-01-01

    We study dyonic soliton and black hole solutions of the su(2) Einstein–Yang–Mills equations in asymptotically anti-de Sitter space. We prove the existence of non-trivial dyonic soliton and black hole solutions in a neighbourhood of the trivial solution. For these solutions the magnetic gauge field function has no zeros and we conjecture that at least some of these non-trivial solutions will be stable. The global existence proof uses local existence results and a nonlinear perturbation argument based on the (Banach space) implicit function theorem. (paper)

  3. Hybrid Approximation of Solutions of Nonlinear Operator Equations and Application to Equation of Hammerstein-Type

    International Nuclear Information System (INIS)

    Ofoedu, Eric U.; Malonza, David M.

    2010-07-01

    In this paper we study the hybrid iterative scheme to find a common element of a set of solutions of generalized mixed equilibrium problem, a set of common fixed points of finite family of weak relatively nonexpansive mapping, and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. Our results extend, improve and generalize the results of several authors which were announced recently. An application of our theorem to the solution of equations of Hammerstein-type is of independent interest. (author)

  4. Determination of the scattering amplitude

    International Nuclear Information System (INIS)

    Gangal, A.D.; Kupsch, J.

    1984-01-01

    The problem to determine the elastic scattering amplitude from the differential cross-section by the unitarity equation is reexamined. We prove that the solution is unique and can be determined by a convergent iteration if the parameter lambda=sin μ of Newton and Martin is bounded by lambda 2 approx.=0.86. The method is based on a fixed point theorem for holomorphic mappings in a complex Banach space. (orig.)

  5. Optimal Control of Evolution Mixed Variational Inclusions

    Energy Technology Data Exchange (ETDEWEB)

    Alduncin, Gonzalo, E-mail: alduncin@geofisica.unam.mx [Universidad Nacional Autónoma de México, Departamento de Recursos Naturales, Instituto de Geofísica (Mexico)

    2013-12-15

    Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory.

  6. Optimal Control of Evolution Mixed Variational Inclusions

    International Nuclear Information System (INIS)

    Alduncin, Gonzalo

    2013-01-01

    Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory

  7. The Existence and Application of Unbounded Connected Components

    Directory of Open Access Journals (Sweden)

    Hua Luo

    2014-01-01

    Full Text Available Let X be a Banach space and Cn a family of connected subsets of R×X. We prove the existence of unbounded components in superior limit of {Cn}, denoted by lim¯ Cn, which have prescribed shapes. As applications, we investigate the global behavior of the set of positive periodic solutions to nonlinear first-order differential equations with delay, which can be used for modeling physiological processes.

  8. Convergence results for a class of abstract continuous descent methods

    Directory of Open Access Journals (Sweden)

    Sergiu Aizicovici

    2004-03-01

    Full Text Available We study continuous descent methods for the minimization of Lipschitzian functions defined on a general Banach space. We establish convergence theorems for those methods which are generated by approximate solutions to evolution equations governed by regular vector fields. Since the complement of the set of regular vector fields is $sigma$-porous, we conclude that our results apply to most vector fields in the sense of Baire's categories.

  9. Differential equations inverse and direct problems

    CERN Document Server

    Favini, Angelo

    2006-01-01

    DEGENERATE FIRST ORDER IDENTIFICATION PROBLEMS IN BANACH SPACES A NONISOTHERMAL DYNAMICAL GINZBURG-LANDAU MODEL OF SUPERCONDUCTIVITY. EXISTENCE AND UNIQUENESS THEOREMSSOME GLOBAL IN TIME RESULTS FOR INTEGRODIFFERENTIAL PARABOLIC INVERSE PROBLEMSFOURTH ORDER ORDINARY DIFFERENTIAL OPERATORS WITH GENERAL WENTZELL BOUNDARY CONDITIONSTUDY OF ELLIPTIC DIFFERENTIAL EQUATIONS IN UMD SPACESDEGENERATE INTEGRODIFFERENTIAL EQUATIONS OF PARABOLIC TYPE EXPONENTIAL ATTRACTORS FOR SEMICONDUCTOR EQUATIONSCONVERGENCE TO STATIONARY STATES OF SOLUTIONS TO THE SEMILINEAR EQUATION OF VISCOELASTICITY ASYMPTOTIC BEHA

  10. The stability of quadratic-reciprocal functional equation

    Science.gov (United States)

    Song, Aimin; Song, Minwei

    2018-04-01

    A new quadratic-reciprocal functional equation f ((k +1 )x +k y )+f ((k +1 )x -k y )=2/f (x )f (y )[(k+1 ) 2f (y )+k2f (x )] [(k+1)2f (y )-k2f (x )] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.

  11. Fiber-wise linear Poisson structures related to W∗-algebras

    Science.gov (United States)

    Odzijewicz, Anatol; Jakimowicz, Grzegorz; Sliżewska, Aneta

    2018-01-01

    In the framework of Banach differential geometry we investigate the fiber-wise linear Poisson structures as well as the Lie groupoid and Lie algebroid structures which are defined in the canonical way by the structure of a W∗-algebra (von Neumann algebra) M. The main role in this theory is played by the complex Banach-Lie groupoid G(M) ⇉ L(M) of partially invertible elements of M over the lattice L(M) of orthogonal projections of M. The Atiyah sequence and the predual Atiyah sequence corresponding to this groupoid are investigated from the point of view of Banach Poisson geometry. In particular we show that the predual Atiyah sequence fits in a short exact sequence of complex Banach sub-Poisson V B-groupoids with G(M) ⇉ L(M) as the side groupoid.

  12. Investigation of the Stability via Shadowing Property

    Directory of Open Access Journals (Sweden)

    Koh Heejeong

    2009-01-01

    Full Text Available The shadowing property is to find an exact solution to an iterated map that remains close to an approximate solution. In this article, using shadowing property, we show the stability of the following equation in normed group: , where , and is a mapping. And we prove that the even mapping which satisfies the above equation is quadratic and also the Hyers-Ulam stability of the functional equation in Banach spaces.

  13. Strong Convergence Theorems for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Nonself Mappings

    Directory of Open Access Journals (Sweden)

    Liang-cai Zhao

    2012-01-01

    Full Text Available The purpose of this paper is to introduce a class of total quasi-ϕ-asymptotically nonexpansive-nonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. The results presented in the paper extend and improve the corresponding results announced by some authors recently.

  14. On spectral subspaces and their applications to automorphism groups

    International Nuclear Information System (INIS)

    Olesen, Dorte

    1974-03-01

    An attempt is made to give a survey of the theory of spectra and spectral subspaces of group representations in an abstract Banach space setting. The theory is applied to the groups of automorphisms of operator algebras (mostly C*-algebras) and some important results of interest for mathematical physicists are proved (restrictions of the bitransposed action, spectral subspaces for the transposed action on a C*-algebra, and positive states and representations of Rsup(n)) [fr

  15. Discrete Weighted Pseudo-Almost Automorphy and Applications

    Directory of Open Access Journals (Sweden)

    Zhinan Xia

    2014-01-01

    Full Text Available We deal with discrete weighted pseudo almost automorphy which extends some classical concepts and systematically explore its properties in Banach space including a composition result. As an application, we establish some sufficient criteria for the existence and uniqueness of the discrete weighted pseudo almost automorphic solutions to the Volterra difference equations of convolution type and also to nonautonomous semilinear difference equations. Some examples are presented to illustrate the main findings.

  16. Iterative method of the parameter variation for solution of nonlinear functional equations

    International Nuclear Information System (INIS)

    Davidenko, D.F.

    1975-01-01

    The iteration method of parameter variation is used for solving nonlinear functional equations in Banach spaces. The authors consider some methods for numerical integration of ordinary first-order differential equations and construct the relevant iteration methods of parameter variation, both one- and multifactor. They also discuss problems of mathematical substantiation of the method, study the conditions and rate of convergence, estimate the error. The paper considers the application of the method to specific functional equations

  17. SEMIGROUPS N TIMES INTEGRATED AND AN APPLICATION TO A PROBLEM OF CAUCHY TYPE

    Directory of Open Access Journals (Sweden)

    Danessa Chirinos Fernández

    2016-06-01

    Full Text Available The theory of semigroups n times integrated is a generalization of strongly continuous semigroups, which was developed from 1984, and is widely used for the study of the existence and uniqueness of problems such Cauchy in which the operator domain is not necessarily dense. This paper presents an application of semigroups n times integrated into a problem of viscoelasticity, which is formulated as a Cauchy problem on a Banach space presents .

  18. Continuous bounded cohomology of locally compact groups

    CERN Document Server

    2001-01-01

    Recent research has repeatedly led to connections between important rigidity questions and bounded cohomology. However, the latter has remained by and large intractable. This monograph introduces the functorial study of the continuous bounded cohomology for topological groups, with coefficients in Banach modules. The powerful techniques of this more general theory have successfully solved a number of the original problems in bounded cohomology. As applications, one obtains, in particular, rigidity results for actions on the circle, for representations on complex hyperbolic spaces and on Teichmüller spaces. A special effort has been made to provide detailed proofs or references in quite some generality.

  19. Field theories on supermanifolds: general formalism, local supersymmetry, and the limit of global supersymmetry

    International Nuclear Information System (INIS)

    Bruzzo, V.

    1986-01-01

    This paper reports briefly on recent investigations concerning the formulation of field theories on supermanifolds. The usual formulations are unsatisfactory from a mathematical viewpoint, hence, this report. A variational theory for fields on a supermanifold is described where the action is a map between Banach spaces. The relationship between the field theory on the supermanifold and a suitably constructed field theory on space-time is also discussed. On-shell local supersymmetry are examined and the limit of global (rigid) supersymmetry is considered. A specific example is given which shows that the limit reproduces the known results

  20. Invariant Measures for Dissipative Dynamical Systems: Abstract Results and Applications

    Science.gov (United States)

    Chekroun, Mickaël D.; Glatt-Holtz, Nathan E.

    2012-12-01

    In this work we study certain invariant measures that can be associated to the time averaged observation of a broad class of dissipative semigroups via the notion of a generalized Banach limit. Consider an arbitrary complete separable metric space X which is acted on by any continuous semigroup { S( t)} t ≥ 0. Suppose that { S( t)} t ≥ 0 possesses a global attractor {{A}}. We show that, for any generalized Banach limit LIM T → ∞ and any probability distribution of initial conditions {{m}_0}, that there exists an invariant probability measure {{m}}, whose support is contained in {{A}}, such that intX \\varphi(x) d{m}(x) = \\underset{t rightarrow infty}LIM1/T int_0^T int_X \\varphi(S(t) x) d{m}_0(x) dt, for all observables φ living in a suitable function space of continuous mappings on X. This work is based on the framework of Foias et al. (Encyclopedia of mathematics and its applications, vol 83. Cambridge University Press, Cambridge, 2001); it generalizes and simplifies the proofs of more recent works (Wang in Disc Cont Dyn Syst 23(1-2):521-540, 2009; Lukaszewicz et al. in J Dyn Diff Eq 23(2):225-250, 2011). In particular our results rely on the novel use of a general but elementary topological observation, valid in any metric space, which concerns the growth of continuous functions in the neighborhood of compact sets. In the case when { S( t)} t ≥ 0 does not possess a compact absorbing set, this lemma allows us to sidestep the use of weak compactness arguments which require the imposition of cumbersome weak continuity conditions and thus restricts the phase space X to the case of a reflexive Banach space. Two examples of concrete dynamical systems where the semigroup is known to be non-compact are examined in detail. We first consider the Navier-Stokes equations with memory in the diffusion terms. This is the so called Jeffery's model which describes certain classes of viscoelastic fluids. We then consider a family of neutral delay differential

  1. On the mild solutions of higher-order differential equations in Banach spaces

    Directory of Open Access Journals (Sweden)

    Nguyen Thanh Lan

    2003-01-01

    Full Text Available For the higher-order abstract differential equation u(n(t=Au(t+f(t, t∈ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace ℳ of BUC(ℝ,E with respect to the above-mentioned equation in terms of solvability of the operator equation AX−Xn=C. As applications, periodicity and almost periodicity of mild solutions are also proved.

  2. Existence and Uniqueness of Solutions for a Discrete Fractional Mixed Type Sum-Difference Equation Boundary Value Problem

    Directory of Open Access Journals (Sweden)

    Weidong Lv

    2015-01-01

    Full Text Available By means of Schauder’s fixed point theorem and contraction mapping principle, we establish the existence and uniqueness of solutions to a boundary value problem for a discrete fractional mixed type sum-difference equation with the nonlinear term dependent on a fractional difference of lower order. Moreover, a suitable choice of a Banach space allows the solutions to be unbounded and two representative examples are presented to illustrate the effectiveness of the main results.

  3. Formal solutions of inverse scattering problems. III

    International Nuclear Information System (INIS)

    Prosser, R.T.

    1980-01-01

    The formal solutions of certain three-dimensional inverse scattering problems presented in papers I and II of this series [J. Math. Phys. 10, 1819 (1969); 17 1175 (1976)] are obtained here as fixed points of a certain nonlinear mapping acting on a suitable Banach space of integral kernels. When the scattering data are sufficiently restricted, this mapping is shown to be a contraction, thereby establishing the existence, uniqueness, and continuous dependence on the data of these formal solutions

  4. On joint spectra of families of unbounded operators

    International Nuclear Information System (INIS)

    Mirotin, A R

    2015-01-01

    We consider several types of joint spectra of a finite set of commuting closed operators in a Banach space. We establish new relations between these spectra (it was previously known only that the Taylor spectrum is contained in the commutant spectrum) and prove spectral mapping theorems in the case of generators of semigroups. Some of these theorems generalize previous results of the author. The results obtained are applied to stability issues for multi-parameter semigroups

  5. Analysis of coupled transport phenomena in concrete at elevated temperatures

    OpenAIRE

    Beneš, Michal; Štefan, Radek; Zeman, Jan

    2010-01-01

    In this paper, we study a non-linear numerical scheme arising from the implicit time discretization of the Ba\\v{z}ant-Thonguthai model for hygro-thermal behavior of concrete at high temperatures. Existence and uniqueness of the time-discrete solution in two dimensions is established using the theory of pseudomonotone operators in Banach spaces. Next, the spatial discretization is accomplished by the conforming finite element method. An illustrative numerical example shows that the numerical m...

  6. A degree theory for a class of perturbed Fredholm maps II

    Directory of Open Access Journals (Sweden)

    Calamai Alessandro

    2006-01-01

    Full Text Available In a recent paper we gave a notion of degree for a class of perturbations of nonlinear Fredholm maps of index zero between real infinite dimensional Banach spaces. Our purpose here is to extend that notion in order to include the degree introduced by Nussbaum for local -condensing perturbations of the identity, as well as the degree for locally compact perturbations of Fredholm maps of index zero recently defined by the first and third authors.

  7. Measures of Noncircularity and Fixed Points of Contractive Multifunctions

    Directory of Open Access Journals (Sweden)

    Marrero Isabel

    2010-01-01

    Full Text Available In analogy to the Eisenfeld-Lakshmikantham measure of nonconvexity and the Hausdorff measure of noncompactness, we introduce two mutually equivalent measures of noncircularity for Banach spaces satisfying a Cantor type property, and apply them to establish a fixed point theorem of Darbo type for multifunctions. Namely, we prove that every multifunction with closed values, defined on a closed set and contractive with respect to any one of these measures, has the origin as a fixed point.

  8. Continuous Disintegrations of Gaussian Processes

    OpenAIRE

    LaGatta, Tom

    2010-01-01

    The goal of this paper is to understand the conditional law of a stochastic process once it has been observed over an interval. To make this precise, we introduce the notion of a continuous disintegration: a regular conditional probability measure which varies continuously in the conditioned parameter. The conditioning is infinite-dimensional in character, which leads us to consider the general case of probability measures in Banach spaces. Our main result is that for a certain quantity $M$ b...

  9. Approximation of a solution for a K-positive definite operator equation

    International Nuclear Information System (INIS)

    Chidume, C.E.; Osilike, M.O.

    1994-11-01

    Let E be a separable q-uniformly smooth Banach space, q > 1, and let A : D(A) is contained in-bar E → E be a K-positive definite operator. Let f is an element of E be arbitrary. An iterative method is constructed which converges strongly to the unique solution of the equation Ax = f. Our result resolves two questions raised in Chidume and Aneke (Applicable Analysis Vol. 50 (1993), p. 293). (author). 13 refs

  10. Jozef Schreier (1909-1943). Biografia

    OpenAIRE

    Maligranda, Lech

    2013-01-01

    Jozef (Josef) Schreier was a Polish mathematician, working in functionalanalysis, group theory and combinatorics. In 1934 he defended Ph.D. thesis On finite basis in topological groups at the University of Jan Kazimierz in Lwow under supervision of Stefan Banach, and was active member of the so-called Lwow School of Mathematics. He published 16 scientific papers and his name is known in mathematics for Schreier spaces, Schreier sets, and Schreier-Ulam theorems. In April 1943, committed suicid...

  11. Uniform stability for time-varying infinite-dimensional discrete linear systems

    International Nuclear Information System (INIS)

    Kubrusly, C.S.

    1988-09-01

    Stability for time-varying discrete linear systems in a Banach space is investigated. On the one hand, it established a fairly complete collection of necessary and sufficient conditions for uniform asymptotic equistability for input-free systems. This includes uniform and strong power equistability, and uniform and strong l p -equistability, among other technical conditions which also play essential role in stability theory. On other hand, it is shown that uniform asymptotic equistability for input-free systems is equivalent to each of the following concepts of uniform stability for forced systems: l p -input l p -state, c o -input c o -state, bounded-input bounded-state, l p>1 -input bounded-state, c sub (o)-input bounded-state, and convergent-input bounded-state; which are also equivalent to their nonuniform counterparts. For time-varying convergent systems, the above is also equivalent to convergent-input convergent-state stability. The proofs presented here are all ''elementary'' in the sense that they are based essentially only on the Banach-Steinhaus theorem. (autor) [pt

  12. Fulltext PDF

    Indian Academy of Sciences (India)

    user1

    Bias expansion of spatial statistics and approximation of differenced lattice point counts. 229. Automorphism. Test rank of an abelian product of a free. Lie algebra and a free abelian Lie algebra. 291. Automorphism group. Semisimple metacyclic group algebras. 379. Banach g-frames. Fusion frames and G-frames in Banach.

  13. Stefan Banach

    Indian Academy of Sciences (India)

    proportions; the rule of three and use of simple proportions; inference; ... inally contained a certain number N of matches, what is the probability that there are exactly k ... Ulam discovered the Monte-Carlo method for statistical sampling.

  14. Goal oriented adaptivity in the IRGNM for parameter identification in PDEs: I. reduced formulation

    International Nuclear Information System (INIS)

    Kaltenbacher, B; Kirchner, A; Veljović, S

    2014-01-01

    In this paper we study adaptive discretization of the iteratively regularized Gauss–Newton method (IRGNM) with an a posteriori (discrepancy principle) choice of the regularization parameter in each Newton step and of the stopping index. We first of all prove convergence and convergence rates under some accuracy requirements formulated in terms of four quantities of interest. Then computation of error estimators for these quantities based on a weighted dual residual method is discussed, which results in an algorithm for adaptive refinement. Finally we extend the results from the Hilbert space setting with quadratic penalty to Banach spaces and general Tikhonov functionals for the regularization of each Newton step. (paper)

  15. Rigorous Numerics for ill-posed PDEs: Periodic Orbits in the Boussinesq Equation

    Science.gov (United States)

    Castelli, Roberto; Gameiro, Marcio; Lessard, Jean-Philippe

    2018-04-01

    In this paper, we develop computer-assisted techniques for the analysis of periodic orbits of ill-posed partial differential equations. As a case study, our proposed method is applied to the Boussinesq equation, which has been investigated extensively because of its role in the theory of shallow water waves. The idea is to use the symmetry of the solutions and a Newton-Kantorovich type argument (the radii polynomial approach) to obtain rigorous proofs of existence of the periodic orbits in a weighted ℓ1 Banach space of space-time Fourier coefficients with exponential decay. We present several computer-assisted proofs of the existence of periodic orbits at different parameter values.

  16. Strong Convergence to Common Fixed Points of a Countable Family of Asymptotically Strictly Quasi-ϕ-Pseudocontractions

    Directory of Open Access Journals (Sweden)

    Wei-Qi Deng

    2013-01-01

    Full Text Available Based on an original idea, namely, a specific way of choosing the indexes of the involved mappings, we propose a new hybrid shrinking iteration scheme for approximating some common fixed points of a countable family of asymptotically strictly quasi-ϕ-pseudocontractions and obtain a strong convergence theorem in the framework of Banach space. Our result extends other authors, related results existing in the current literature. As application, an iterative solution to a system of equilibrium problems is provided.

  17. Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities

    Directory of Open Access Journals (Sweden)

    Chidume CO

    2008-01-01

    Full Text Available Abstract Let be a real -uniformly smooth Banach space with constant , . Let and be a nonexpansive map and an -strongly accretive map which is also -Lipschitzian, respectively. Let be a real sequence in that satisfies the following condition: and . For and , define a sequence iteratively in by , , . Then, converges strongly to the unique solution of the variational inequality problem (search for such that for all , where . A convergence theorem related to finite family of nonexpansive maps is also proved.

  18. Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems

    Directory of Open Access Journals (Sweden)

    Kriengsak Wattanawitoon

    2011-01-01

    Full Text Available We prove strong and weak convergence theorems of modified hybrid proximal-point algorithms for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of solution of the variational inequality operators of an inverse strongly monotone in a Banach space under different conditions. Moreover, applications to complementarity problems are given. Our results modify and improve the recently announced ones by Li and Song (2008 and many authors.

  19. On the invertibility of elementary operators

    OpenAIRE

    Boudi, Nadia; Bračič, Janko

    2013-01-01

    Let $\\mathscr{X}$ be a complex Banach space and $\\mathcal{L}(\\mathscr{X})$ be the algebra of all bounded linear operators on $\\mathscr{X}$. For a given elementary operator $\\Phi$ of length $2$ on $\\mathcal{L}(\\mathscr{X})$, we determine necessary and sufficient conditions for the existence of a solution of the equation ${\\rm X} \\Phi=0$ in the algebra of all elementary operators on $\\mathcal{L}(\\mathscr{X})$. Our approach allows us to characterize some invertible elementary operators of length...

  20. Polynomially Riesz elements | Živković-Zlatanović | Quaestiones ...

    African Journals Online (AJOL)

    A Banach algebra element ɑ ∈ A is said to be "polynomially Riesz", relative to the homomorphism T : A → B, if there exists a nonzero complex polynomial p(z) such that the image Tp ∈ B is quasinilpotent. Keywords: Homomorphism of Banach algebras, polynomially Riesz element, Fredholm spectrum, Browder element, ...

  1. Operator theory

    CERN Document Server

    2015-01-01

    A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis, mathematical physics, and electrical engineering, to name a few. Fascinating new applications and directions regularly appear, such as operator spaces, free probability, and applications to Clifford analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and more sections are planned, to complete the picture. We hope you enjoy the reading, and profit from this endeavor.

  2. The approximation of flows

    International Nuclear Information System (INIS)

    Robinson, D.W.

    1975-11-01

    Let U,V be two strongly continuous one-parameter groups of bounded operators on a Banach space X with corresponding infinitesimal operators S, T. It is proved that: //U(t)-V(t)//=0(t), t→0, if, and only if, U=V; //U(t)-V(t)//=0 (t.exp.α), t→0, with 0 -1 where OMEGA, P, are bounded operators on X such that //U(t)OMEGA-OMEGA.U(t)//=0(t.exp.α), //U(t)P-PU(t)//=0(t.exp.α); t→0; //U(t)-V(t)//=0(t) if, and only if, S*-T* has a bounded extension to X*. Further results of this nature are inferred for semigroups, reflexive spaces, Hilbert spaces, and von Neumann algebras [fr

  3. Vector-valued almost convergence and classical properties in ...

    Indian Academy of Sciences (India)

    So, Banach limits are legitimate extensions of the limit function on c. In. [14], Lorentz made use of the concept of Banach limit to introduce the notion of 'almost convergence'. DEFINITION 1.2 [14]. A bounded sequence (xn)n∈N ∈ l∞ is called almost convergent exactly when there exists a number y ∈ R (called the almost ...

  4. A hyperpower iterative method for computing the generalized Drazin ...

    Indian Academy of Sciences (India)

    Shwetabh Srivastava

    [6, 7]. A number of direct and iterative methods for com- putation of the Drazin inverse were developed in [8–12]. Its extension to Banach algebras is known as the generalized Drazin inverse and was established in [13]. Let J denote the complex. Banach algebra with the unit 1. The generalized Drazin inverse of an element ...

  5. Download this PDF file

    African Journals Online (AJOL)

    for 2n+1 > O. 2n-1, (ne N* fixed), when the skeletons of the closed ideals under consideration are at most countable. Keywords: Closed Ideals, Banach Algebras, K-algebra, Skeleton, Inner factors, Standard. Ideals. RESUME. Dans cet article nous décrivons completement les idéaux fermés de algebre de Banach D de ...

  6. Exponentially Convergent Algorithms for Abstract Differential Equations

    CERN Document Server

    Gavrilyuk, Ivan; Vasylyk, Vitalii

    2011-01-01

    This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for the practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as the partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which

  7. Weighted asymptotic behavior of solutions to semilinear integro-differential equations in Banach spaces

    Directory of Open Access Journals (Sweden)

    Yan-Tao Bian

    2014-04-01

    Full Text Available In this article, we study weighted asymptotic behavior of solutions to the semilinear integro-differential equation $$ u'(t=Au(t+\\alpha\\int_{-\\infty}^{t}e^{-\\beta(t-s}Au(sds+f(t,u(t, \\quad t\\in \\mathbb{R}, $$ where $\\alpha, \\beta \\in \\mathbb{R}$, with $\\beta > 0, \\alpha \

  8. Integral Boundary Value Problems for Fractional Impulsive Integro Differential Equations in Banach Spaces

    Directory of Open Access Journals (Sweden)

    A. Anguraj

    2014-02-01

    Full Text Available We study in this paper,the existence of solutions for fractional integro differential equations with impulsive and integral conditions by using fixed point method. We establish the Sufficient conditions and unique solution for given problem. An Example is also explained to the main results.

  9. Generalized linear differential equations in a Banach space : continuous dependence on a parameter

    Czech Academy of Sciences Publication Activity Database

    Monteiro, G.A.; Tvrdý, Milan

    2013-01-01

    Roč. 33, č. 1 (2013), s. 283-303 ISSN 1078-0947 Institutional research plan: CEZ:AV0Z10190503 Keywords : generalized differential equations * continuous dependence * Kurzweil-Stieltjes integral Subject RIV: BA - General Mathematics Impact factor: 0.923, year: 2013 http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=7615

  10. Compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions

    Directory of Open Access Journals (Sweden)

    Davood Alimohammadi

    2014-10-01

    Full Text Available We characterize compact composition operators on real Banachspaces of complex-valued bounded Lipschitz functions on metricspaces, not necessarily compact, with Lipschitz involutions anddetermine their spectra.

  11. On n-weak amenability of Rees semigroup algebras

    Indian Academy of Sciences (India)

    semigroups. In this work, we shall consider this class of Banach algebras. We examine the n-weak amenability of some semigroup algebras, and give an easier example of a Banach algebra which is n-weakly amenable if n is odd. Let L1(G) be the group algebra of a locally compact group G (§3.3 of [3]). Then Johnson.

  12. Metric regularity and subdifferential calculus

    International Nuclear Information System (INIS)

    Ioffe, A D

    2000-01-01

    The theory of metric regularity is an extension of two classical results: the Lyusternik tangent space theorem and the Graves surjection theorem. Developments in non-smooth analysis in the 1980s and 1990s paved the way for a number of far-reaching extensions of these results. It was also well understood that the phenomena behind the results are of metric origin, not connected with any linear structure. At the same time it became clear that some basic hypotheses of the subdifferential calculus are closely connected with the metric regularity of certain set-valued maps. The survey is devoted to the metric theory of metric regularity and its connection with subdifferential calculus in Banach spaces

  13. Existence, regularity and representation of solutions of time fractional wave equations

    Directory of Open Access Journals (Sweden)

    Valentin Keyantuo

    2017-09-01

    Full Text Available We study the solvability of the fractional order inhomogeneous Cauchy problem $$ \\mathbb{D}_t^\\alpha u(t=Au(t+f(t, \\quad t>0,\\;1<\\alpha\\le 2, $$ where A is a closed linear operator in some Banach space X and $f:[0,\\infty\\to X$ a given function. Operator families associated with this problem are defined and their regularity properties are investigated. In the case where A is a generator of a $\\beta$-times integrated cosine family $(C_\\beta(t$, we derive explicit representations of mild and classical solutions of the above problem in terms of the integrated cosine family. We include applications to elliptic operators with Dirichlet, Neumann or Robin type boundary conditions on $L^p$-spaces and on the space of continuous functions.

  14. Advanced functional evolution equations and inclusions

    CERN Document Server

    Benchohra, Mouffak

    2015-01-01

    This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks. This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.

  15. The limit distribution of the maximum increment of a random walk with regularly varying jump size distribution

    DEFF Research Database (Denmark)

    Mikosch, Thomas Valentin; Rackauskas, Alfredas

    2010-01-01

    In this paper, we deal with the asymptotic distribution of the maximum increment of a random walk with a regularly varying jump size distribution. This problem is motivated by a long-standing problem on change point detection for epidemic alternatives. It turns out that the limit distribution...... of the maximum increment of the random walk is one of the classical extreme value distributions, the Fréchet distribution. We prove the results in the general framework of point processes and for jump sizes taking values in a separable Banach space...

  16. The history of a general criterium on spaceability

    Directory of Open Access Journals (Sweden)

    Sánchez Víctor M.

    2017-03-01

    Full Text Available There are just a few general criteria on spaceability. This survey paper is the history of one of the first ones. Let I1 and I2 be arbitrary operator ideals and E and F be Banach spaces. The spaceability of the set of operators I1(E, F\\ I2(E, F is studied. Before stating the criterium, the paper summarizes the main results about lineability and spaceability of differences between particular operator ideals obtained in recent years. They are the seed of the ideas contained in the general criterium.

  17. A class of quasilinear parabolic equations with infinite delay and application to a problem of viscoelasticity

    Science.gov (United States)

    Renardy, M.

    A semigroup approach to differential-delay equations is developed which reduces such equations to ordinary differential equations on a Banach space of histories and seems more suitable for certain partial integro-differential equations than the standard theory. The method is applied to prove a local-time existence theorem for equations of the form utt = g( uxt, uxt) x, where {∂g}/{∂u xt} > 0 . On a formal level, it is demonstrated that the stretching of filaments of viscoelastic liquids can be described by an equation of this form.

  18. Iterative solutions of nonlinear equations with strongly accretive or strongly pseudocontractive maps

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1994-03-01

    Let E be a real q-uniformly smooth Banach space. Suppose T is a strongly pseudo-contractive map with open domain D(T) in E. Suppose further that T has a fixed point in D(T). Under various continuity assumptions on T it is proved that each of the Mann iteration process or the Ishikawa iteration method converges strongly to the unique fixed point of T. Related results deal with iterative solutions of nonlinear operator equations involving strongly accretive maps. Explicit error estimates are also provided. (author). 38 refs

  19. Analytic semigroups and optimal regularity in parabolic problems

    CERN Document Server

    Lunardi, Alessandra

    2012-01-01

    The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in p

  20. Existence of solutions for quasilinear random impulsive neutral differential evolution equation

    Directory of Open Access Journals (Sweden)

    B. Radhakrishnan

    2018-07-01

    Full Text Available This paper deals with the existence of solutions for quasilinear random impulsive neutral functional differential evolution equation in Banach spaces and the results are derived by using the analytic semigroup theory, fractional powers of operators and the Schauder fixed point approach. An application is provided to illustrate the theory. Keywords: Quasilinear differential equation, Analytic semigroup, Random impulsive neutral differential equation, Fixed point theorem, 2010 Mathematics Subject Classification: 34A37, 47H10, 47H20, 34K40, 34K45, 35R12

  1. On distributed parameter control systems in the abnormal case and in the case of nonoperator equality constraints

    Directory of Open Access Journals (Sweden)

    Urszula Ledzewicz

    1993-01-01

    Full Text Available In this paper, a general distributed parameter control problem in Banach spaces with integral cost functional and with given initial and terminal data is considered. An extension of the Dubovitskii-Milyutin method to the case of nonregular operator equality constraints, based on Avakov's generalization of the Lusternik theorem, is presented. This result is applied to obtain an extension of the Extremum Principle for the case of abnormal optimal control problems. Then a version of this problem with nonoperator equality constraints is discussed and the Extremum Principle for this problem is presented.

  2. Paratingent Derivative Applied to the Measure of the Sensitivity in Multiobjective Differential Programming

    Directory of Open Access Journals (Sweden)

    F. García

    2013-01-01

    Full Text Available We analyse the sensitivity of differential programs of the form subject to where and are maps whose respective images lie in ordered Banach spaces. Following previous works on multiobjective programming, the notion of -optimal solution is used. The behaviour of some nonsingleton sets of -optimal solutions according to changes of the parameter in the problem is analysed. The main result of the work states that the sensitivity of the program is measured by a Lagrange multiplier plus a projection of its derivative. This sensitivity is measured by means of the paratingent derivative.

  3. Infinite-dimensional Z2sup(k)-supermanifolds

    International Nuclear Information System (INIS)

    Molotkov, V.

    1984-10-01

    In this paper the theory of finite-dimensional supermanifolds of Berezin, Leites and Kostant is generalized in two directions. First, we introduce infinite-dimensional supermanifolds ''locally isomorphic'' to arbitrary Banach (or, more generally, locally convex) superspaces. This is achieved by considering supermanifolds as functors (equipped with some additional structure) from the category of finite-dimensional Grassman superalgebras into the category of the corresponding smooth manifolds (Banach or locally convex). As examples, flag supermanifolds of Banach superspaces as well as unitary supergroups of Hilbert superspaces are constructed. Second, we define ''generalized'' supermanifolds, graded by Abelian groups Z 2 sup(k), instead of the group Z 2 (Z 2 sup(k)-supermanifolds). The corresponding superfields, describing, potentially, particles with more general statistics than Bose + Fermi, generally speaking, turn out to have an infinite number of components. (author)

  4. Topological fixed point theory for singlevalued and multivalued mappings and applications

    CERN Document Server

    Ben Amar, Afif

    2016-01-01

    This is a monograph covering topological fixed point theory for several classes of single and multivalued maps. The authors begin by presenting basic notions in locally convex topological vector spaces. Special attention is then devoted to weak compactness, in particular to the theorems of Eberlein–Šmulian, Grothendick and Dunford–Pettis. Leray–Schauder alternatives and eigenvalue problems for decomposable single-valued nonlinear weakly compact operators in Dunford–Pettis spaces are considered, in addition to some variants of Schauder, Krasnoselskii, Sadovskii, and Leray–Schauder type fixed point theorems for different classes of weakly sequentially continuous operators on general Banach spaces. The authors then proceed with an examination of Sadovskii, Furi–Pera, and Krasnoselskii fixed point theorems and nonlinear Leray–Schauder alternatives in the framework of weak topologies and involving multivalued mappings with weakly sequentially closed graph. These results are formulated in terms of ax...

  5. A Note on Generalized Hardy-Sobolev Inequalities

    Directory of Open Access Journals (Sweden)

    T. V. Anoop

    2013-01-01

    Full Text Available We are concerned with finding a class of weight functions g so that the following generalized Hardy-Sobolev inequality holds: ∫Ωgu2≤C∫Ω|∇u|2,   u∈H01(Ω, for some C>0, where Ω is a bounded domain in ℝ2. By making use of Muckenhoupt condition for the one-dimensional weighted Hardy inequalities, we identify a rearrangement invariant Banach function space so that the previous integral inequality holds for all weight functions in it. For weights in a subspace of this space, we show that the best constant in the previous inequality is attained. Our method gives an alternate way of proving the Moser-Trudinger embedding and its refinement due to Hansson.

  6. The spectral method and ergodic theorems for general Markov chains

    International Nuclear Information System (INIS)

    Nagaev, S V

    2015-01-01

    We study the ergodic properties of Markov chains with an arbitrary state space and prove a geometric ergodic theorem. The method of the proof is new: it may be described as an operator method. Our main result is an ergodic theorem for Harris-Markov chains in the case when the return time to some fixed set has finite expectation. Our conditions for the transition function are more general than those used by Athreya-Ney and Nummelin. Unlike them, we impose restrictions not on the original transition function but on the transition function of an embedded Markov chain constructed from the return times to the fixed set mentioned above. The proof uses the spectral theory of linear operators on a Banach space

  7. Semi-bounded partial differential operators

    CERN Document Server

    Cialdea, Alberto

    2014-01-01

    This book examines the conditions for the semi-boundedness of partial differential operators, which are interpreted in different ways. For example, today we know a great deal about L2-semibounded differential and pseudodifferential operators, although their complete characterization in analytic terms still poses difficulties, even for fairly simple operators. In contrast, until recently almost nothing was known about analytic characterizations of semi-boundedness for differential operators in other Hilbert function spaces and in Banach function spaces. This book works to address that gap. As such, various types of semi-boundedness are considered and a number of relevant conditions which are either necessary and sufficient or best possible in a certain sense are presented. The majority of the results reported on are the authors’ own contributions.

  8. Eigenvalue for Densely Defined Perturbations of Multivalued Maximal Monotone Operators in Reflexive Banach Spaces

    Directory of Open Access Journals (Sweden)

    Boubakari Ibrahimou

    2013-01-01

    maximal monotone with and . Using the topological degree theory developed by Kartsatos and Quarcoo we study the eigenvalue problem where the operator is a single-valued of class . The existence of continuous branches of eigenvectors of infinite length then could be easily extended to the case where the operator is multivalued and is investigated.

  9. On linear isometries of Banach lattices in C0( ) C0( ) C0( )-spaces

    Indian Academy of Sciences (India)

    elements are the same point in , and hence we must have T (S) = T (S ), which poses a real difficulty concerning the ..... 1S nor its image by a. A(S) (which is (A1 )|S in accordance with (6.1)) depend on the particular order we choose for the set S. We refer to S ↦→ a. A(S)(1S) as the action of the family a. A on the units 1S, ...

  10. A semigroup approach to the strong ergodic theorem of the multistate stable population process.

    Science.gov (United States)

    Inaba, H

    1988-01-01

    "In this paper we first formulate the dynamics of multistate stable population processes as a partial differential equation. Next, we rewrite this equation as an abstract differential equation in a Banach space, and solve it by using the theory of strongly continuous semigroups of bounded linear operators. Subsequently, we investigate the asymptotic behavior of this semigroup to show the strong ergodic theorem which states that there exists a stable distribution independent of the initial distribution. Finally, we introduce the dual problem in order to obtain a logical definition for the reproductive value and we discuss its applications." (SUMMARY IN FRE) excerpt

  11. A New Multi-Step Iterative Algorithm for Approximating Common Fixed Points of a Finite Family of Multi-Valued Bregman Relatively Nonexpansive Mappings

    Directory of Open Access Journals (Sweden)

    Wiyada Kumam

    2016-05-01

    Full Text Available In this article, we introduce a new multi-step iteration for approximating a common fixed point of a finite class of multi-valued Bregman relatively nonexpansive mappings in the setting of reflexive Banach spaces. We prove a strong convergence theorem for the proposed iterative algorithm under certain hypotheses. Additionally, we also use our results for the solution of variational inequality problems and to find the zero points of maximal monotone operators. The theorems furnished in this work are new and well-established and generalize many well-known recent research works in this field.

  12. On an abstract evolution equation with a spectral operator of scalar type

    Directory of Open Access Journals (Sweden)

    Marat V. Markin

    2002-01-01

    Full Text Available It is shown that the weak solutions of the evolution equation y′(t=Ay(t, t∈[0,T (0Banach space X, defined by Ball (1977, are given by the formula y(t=e tAf, t∈[0,T, with the exponentials understood in the sense of the operational calculus for such operators and the set of the initial values, f's, being ∩ 0≤t

  13. Controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with delay and Poisson jumps

    Directory of Open Access Journals (Sweden)

    Diem Dang Huan

    2015-12-01

    Full Text Available The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.

  14. Criticality problems in energy dependent neutron transport theory

    International Nuclear Information System (INIS)

    Victory, H.D. Jr.

    1979-01-01

    The criticality problem is considered for energy dependent neutron transport in an isotropically scattering, homogeneous slab. Under a positivity assumption on the scattering kernel, an expression can be found relating the thickness of the slab to a parameter characterizing production by fission. This is accomplished by exploiting the Perron-Frobenius-Jentsch characterization of positive operators (i.e. those leaving invariant a normal, reproducing cone in a Banach space). It is pointed out that those techniques work for classes of multigroup problems were the Case singular eigenfunction approach is not as feasible as in the one-group theory, which is also analyzed

  15. A cluster expansion approach to exponential random graph models

    International Nuclear Information System (INIS)

    Yin, Mei

    2012-01-01

    The exponential family of random graphs are among the most widely studied network models. We show that any exponential random graph model may alternatively be viewed as a lattice gas model with a finite Banach space norm. The system may then be treated using cluster expansion methods from statistical mechanics. In particular, we derive a convergent power series expansion for the limiting free energy in the case of small parameters. Since the free energy is the generating function for the expectations of other random variables, this characterizes the structure and behavior of the limiting network in this parameter region

  16. Existence and uniqueness of mild and classical solutions of impulsive evolution equations

    Directory of Open Access Journals (Sweden)

    Annamalai Anguraj

    2005-10-01

    Full Text Available We consider the non-linear impulsive evolution equation $$displaylines{ u'(t=Au(t+f(t,u(t,Tu(t,Su(t, quad 0Banach space $ X$, where $ A $ is the infinitesimal generator of a $C_0 $ semigroup. We study the existence and uniqueness of the mild solutions of the evolution equation by using semigroup theory and then show that the mild solutions give rise to a classical solutions.

  17. Dichotomy and almost automorphic solution of difference system

    Directory of Open Access Journals (Sweden)

    Samuel Castillo

    2013-06-01

    Full Text Available We study almost automorphic solutions of recurrence relations with values in a Banach space $V$ for quasilinear almost automorphic difference systems. Its linear part is a constant bounded linear operator $\\varLambda$ defined on $V$ satisfying an exponential dichotomy. We study the existence of almost automorphic solutions of the non-homogeneous linear difference equation and to quasilinear difference equation. Assuming global Lipschitz type conditions, we obtain Massera type results for these abstract systems. The case where the eigenvalues $\\lambda$ verify $\\left|\\lambda\\right|=1$ is also treated. An application to differential equations with piecewise constant argument is given.

  18. Basic operator theory

    CERN Document Server

    Gohberg, Israel

    2001-01-01

    rii application of linear operators on a Hilbert space. We begin with a chapter on the geometry of Hilbert space and then proceed to the spectral theory of compact self adjoint operators; operational calculus is next presented as a nat­ ural outgrowth of the spectral theory. The second part of the text concentrates on Banach spaces and linear operators acting on these spaces. It includes, for example, the three 'basic principles of linear analysis and the Riesz­ Fredholm theory of compact operators. Both parts contain plenty of applications. All chapters deal exclusively with linear problems, except for the last chapter which is an introduction to the theory of nonlinear operators. In addition to the standard topics in functional anal­ ysis, we have presented relatively recent results which appear, for example, in Chapter VII. In general, in writ­ ing this book, the authors were strongly influenced by re­ cent developments in operator theory which affected the choice of topics, proofs and exercises. One ...

  19. Existence of Lipschitz selections of the Steiner map

    Science.gov (United States)

    Bednov, B. B.; Borodin, P. A.; Chesnokova, K. V.

    2018-02-01

    This paper is concerned with the problem of the existence of Lipschitz selections of the Steiner map {St}_n, which associates with n points of a Banach space X the set of their Steiner points. The answer to this problem depends on the geometric properties of the unit sphere S(X) of X, its dimension, and the number n. For n≥slant 4 general conditions are obtained on the space X under which {St}_n admits no Lipschitz selection. When X is finite dimensional it is shown that, if n≥slant 4 is even, the map {St}_n has a Lipschitz selection if and only if S(X) is a finite polytope; this is not true if n≥slant 3 is odd. For n=3 the (single-valued) map {St}_3 is shown to be Lipschitz continuous in any smooth strictly-convex two-dimensional space; this ceases to be true in three-dimensional spaces. Bibliography: 21 titles.

  20. Linear functional analysis for scientists and engineers

    CERN Document Server

    Limaye, Balmohan V

    2016-01-01

    This book provides a concise and meticulous introduction to functional analysis. Since the topic draws heavily on the interplay between the algebraic structure of a linear space and the distance structure of a metric space, functional analysis is increasingly gaining the attention of not only mathematicians but also scientists and engineers. The purpose of the text is to present the basic aspects of functional analysis to this varied audience, keeping in mind the considerations of applicability. A novelty of this book is the inclusion of a result by Zabreiko, which states that every countably subadditive seminorm on a Banach space is continuous. Several major theorems in functional analysis are easy consequences of this result. The entire book can be used as a textbook for an introductory course in functional analysis without having to make any specific selection from the topics presented here. Basic notions in the setting of a metric space are defined in terms of sequences. These include total boundedness, c...

  1. The Navier-Stokes equations an elementary functional analytic approach

    CERN Document Server

    Sohr, Hermann

    2001-01-01

    The primary objective of this monograph is to develop an elementary and self­ contained approach to the mathematical theory of a viscous incompressible fluid in a domain 0 of the Euclidean space ]Rn, described by the equations of Navier­ Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers' convenience, in the first two chapters we collect without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain O. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n = 2,3 that are also most significant from the physical point of view. For mathematical generality, we will develop the lin­ earized theory for all n 2 2. Although the functional-analytic approach developed here is, in principle, known ...

  2. Harmonic analysis

    CERN Document Server

    Helson, Henry

    2010-01-01

    This second edition has been enlarged and considerably rewritten. Among the new topics are infinite product spaces with applications to probability, disintegration of measures on product spaces, positive definite functions on the line, and additional information about Weyl's theorems on equidistribution. Topics that have continued from the first edition include Minkowski's theorem, measures with bounded powers, idempotent measures, spectral sets of bounded functions and a theorem of Szego, and the Wiener Tauberian theorem. Readers of the book should have studied the Lebesgue integral, the elementary theory of analytic and harmonic functions, and the basic theory of Banach spaces. The treatment is classical and as simple as possible. This is an instructional book, not a treatise. Mathematics students interested in analysis will find here what they need to know about Fourier analysis. Physicists and others can use the book as a reference for more advanced topics.

  3. Partial stabilization and control of distributed parameter systems with elastic elements

    CERN Document Server

    Zuyev, Alexander L

    2015-01-01

     This monograph provides a rigorous treatment of problems related to partial asymptotic stability and controllability for models of flexible structures described by coupled nonlinear ordinary and partial differential equations or equations in abstract spaces. The text is self-contained, beginning with some basic results from the theory of continuous semigroups of operators in Banach spaces. The problem of partial asymptotic stability with respect to a continuous functional is then considered for a class of abstract multivalued systems on a metric space. Next, the results of this study are applied to the study of a rotating body with elastic attachments. Professor Zuyev demonstrates that the equilibrium cannot be made strongly asymptotically stable in the general case, motivating consideration of the problem of partial stabilization with respect to the functional that represents “averaged” oscillations. The book’s focus moves on to spillover analysis for infinite-dimensional systems with finite-dimensio...

  4. Collage-based approaches for elliptic partial differential equations inverse problems

    Science.gov (United States)

    Yodzis, Michael; Kunze, Herb

    2017-01-01

    The collage method for inverse problems has become well-established in the literature in recent years. Initial work developed a collage theorem, based upon Banach's fixed point theorem, for treating inverse problems for ordinary differential equations (ODEs). Amongst the subsequent work was a generalized collage theorem, based upon the Lax-Milgram representation theorem, useful for treating inverse problems for elliptic partial differential equations (PDEs). Each of these two different approaches can be applied to elliptic PDEs in one space dimension. In this paper, we explore and compare how the two different approaches perform for the estimation of the diffusivity for a steady-state heat equation.

  5. Existence of solutions to boundary value problem of fractional differential equations with impulsive

    Directory of Open Access Journals (Sweden)

    Weihua JIANG

    2016-12-01

    Full Text Available In order to solve the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line, the existence of solutions to the boundary problem is specifically studied. By defining suitable Banach spaces, norms and operators, using the properties of fractional calculus and applying the contraction mapping principle and Krasnoselskii's fixed point theorem, the existence of solutions for the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line is proved, and examples are given to illustrate the existence of solutions to this kind of equation boundary value problems.

  6. Israel Seminar 1996–2000

    CERN Document Server

    Schechtman, Gideon

    2000-01-01

    This volume of original research papers from the Israeli GAFA seminar during the years 1996-2000 not only reports on more traditional directions of Geometric Functional Analysis, but also reflects on some of the recent new trends in Banach Space Theory and related topics. These include the tighter connection with convexity and the resulting added emphasis on convex bodies that are not necessarily centrally symmetric, and the treatment of bodies which have only very weak convex-like structure. Another topic represented here is the use of new probabilistic tools; in particular transportation of measure methods and new inequalities emerging from Poincaré-like inequalities.

  7. Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)

    CERN Document Server

    1994-01-01

    1) Phase Transitions, represented by generalizations of the classical Stefan problem. This is studied by Kenmochi and Rodrigues by means of variational techniques. 2) Hysteresis Phenomena. Some alloys exhibit shape memory effects, corresponding to a stress-strain relation which strongly depends on temperature; mathematical physical aspects are treated in Müller's paper. In a general framework, hysteresis can be described by means of hysteresis operators in Banach spaces of time dependent functions; their properties are studied by Brokate. 3) Numerical analysis. Several models of the phenomena above can be formulated in terms of nonlinear parabolic equations. Here Verdi deals with the most updated approximation techniques.

  8. A new iteration process for finite families of generalized lipschitz pseudo-contractive and generalized lipschitz accretive mappings

    International Nuclear Information System (INIS)

    Chidume, C.E.; Ofoedu, E.U.

    2007-07-01

    In this paper, we introduce a new iteration process and prove that it converges strongly to a common fixed point for a finite family of generalized Lipschitz nonlinear mappings in a real reflexive Banach space E with a with uniformly Gateaux differentiable norm if at least one member of the family is pseudo-contractive. We also prove that a slight modification of the process converges to a common zero for a finite family of generalized Lipschitz accretive operators defined on E. Results for nonexpansive families are obtained as easy corollaries. Finally, our new iteration process and our method of proof are of independent interest. (author)

  9. The Navier-Stokes equations an elementary functional analytic approach

    CERN Document Server

    Sohr, Hermann

    2001-01-01

    The primary objective of this monograph is to develop an elementary and self-contained approach to the mathematical theory of a viscous, incompressible fluid in a domain of the Euclidean space, described by the equations of Navier-Stokes. Moreover, the theory is presented for completely general domains, in particular, for arbitrary unbounded, nonsmooth domains. Therefore, restriction was necessary to space dimensions two and three, which are also the most significant from a physical point of view. For mathematical generality, however, the linearized theory is expounded for general dimensions higher than one. Although the functional analytic approach developed here is, in principle, known to specialists, the present book fills a gap in the literature providing a systematic treatment of a subject that has been documented until now only in fragments. The book is mainly directed to students familiar with basic tools in Hilbert and Banach spaces. However, for the readers’ convenience, some fundamental properties...

  10. Semi-inner-products in Banach Spaces with Applications to Regularized Learning, Sampling, and Sparse Approximation

    Science.gov (United States)

    2016-03-13

    7.00 8.00 Praveen K. Yenduri, Anna C. Gilbert, Jun Zhang. Integrate-and-fire neuron modeled as a low-rate sparse time-encoding device, 2012 Third...International Conference on Intelligent Control and Information Processing (ICICIP). 15-JUL- 12, Dalian, China. : , Praveen K. Yenduri, Anna C. Gilbert

  11. Ecole d'été de probabilités de Saint-Flour XXXIII

    CERN Document Server

    2007-01-01

    Since the impressive works of Talagrand, concentration inequalities have been recognized as fundamental tools in several domains such as geometry of Banach spaces or random combinatorics. They also turn out to be essential tools to develop a non-asymptotic theory in statistics, exactly as the central limit theorem and large deviations are known to play a central part in the asymptotic theory. An overview of a non-asymptotic theory for model selection is given here and some selected applications to variable selection, change points detection and statistical learning are discussed. This volume reflects the content of the course given by P. Massart in St. Flour in 2003. It is mostly self-contained and accessible to graduate students.

  12. Fixed points for alpha-psi contractive mappings with an application to quadratic integral equations

    Directory of Open Access Journals (Sweden)

    Bessem Samet

    2014-06-01

    Full Text Available Recently, Samet et al [24] introduced the concept of alpha-psi contractive mappings and studied the existence of fixed points for such mappings. In this article, we prove three fixed point theorems for this class of operators in complete metric spaces. Our results extend the results in [24] and well known fixed point theorems due to Banach, Kannan, Chatterjea, Zamfirescu, Berinde, Suzuki, Ciric, Nieto, Lopez, and many others. We prove that alpha-psi contractions unify large classes of contractive type operators, whose fixed points can be obtained by means of the Picard iteration. Finally, we utilize our results to discuss the existence and uniqueness of solutions to a class of quadratic integral equations.

  13. On Bi-Dimensional Second µ-Variation

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    Ereú Jurancy

    2014-12-01

    Full Text Available In this paper, we present a generalization of the notion of bounded slope variation for functions defined on a rectangle Iba in ℝ2. Given a strictly increasing function µ-defined in a closed real interval, we introduce the class BVµ,2 (Iba , of functions of bounded second µ-variation on Iba ; and show that this class can be equipped with a norm with respect to which it is a Banach space. We also deal with the important case of factorizable functions in BVµ,2 (Iba and finally we exhibit a relation between this class and the one of double Riemann-Stieltjes integrals of functions of bi-dimensional bounded variation.

  14. Systems of evolution equations and the singular perturbation method

    International Nuclear Information System (INIS)

    Mika, J.

    Several fundamental theorems are presented important for the solution of linear evolution equations in the Banach space. The algorithm is deduced extending the solution of the system of singularly perturbed evolution equations into an asymptotic series with respect to a small positive parameter. The asymptotic convergence is shown of an approximate solution to the accurate solution. Singularly perturbed evolution equations of the resonance type were analysed. The special role is considered of the asymptotic equivalence of P1 equations obtained as the first order approximation if the spherical harmonics method is applied to the linear Boltzmann equation, and the diffusion equations of the linear transport theory where the small parameter approaches zero. (J.B.)

  15. Computing fixed points of nonexpansive mappings by $\\alpha$-dense curves

    Directory of Open Access Journals (Sweden)

    G. García

    2017-08-01

    Full Text Available Given a multivalued nonexpansive mapping defined on a convex and compact set of a Banach space, with values in the class of convex and compact subsets of its domain, we present an iteration scheme which (under suitable conditions converges to a fixed point of such mapping. This new iteration provides us another method to approximate the fixed points of a singlevalued nonexpansive mapping, defined on a compact and convex set into itself. Moreover, the conditions for the singlevalued case are less restrictive than for the multivalued case. Our main tool will be the so called $\\alpha$-dense curves, which will allow us to construct such iterations. Some numerical examples are provided to illustrate our results.

  16. Complete convergence for weighted sums of arrays of random elements

    Directory of Open Access Journals (Sweden)

    Robert Lee Taylor

    1983-01-01

    Full Text Available Let {Xnk:k,n=1,2,…} be an array of row-wise independent random elements in a separable Banach space. Let {ank:k,n=1,2,…} be an array of real numbers such that ∑k=1∞|ank|≤1 and ∑n=1∞exp(−α/An<∞ for each α ϵ R+ where An=∑k=1∞ank2. The complete convergence of ∑k=1∞ankXnk is obtained under varying moment and distribution conditions on the random elements. In particular, laws of large numbers follow for triangular arrays of random elements, and consistency of the kernel density estimates is obtained from these results.

  17. Variational analysis of regular mappings theory and applications

    CERN Document Server

    Ioffe, Alexander D

    2017-01-01

    This monograph offers the first systematic account of (metric) regularity theory in variational analysis. It presents new developments alongside classical results and demonstrates the power of the theory through applications to various problems in analysis and optimization theory. The origins of metric regularity theory can be traced back to a series of fundamental ideas and results of nonlinear functional analysis and global analysis centered around problems of existence and stability of solutions of nonlinear equations. In variational analysis, regularity theory goes far beyond the classical setting and is also concerned with non-differentiable and multi-valued operators. The present volume explores all basic aspects of the theory, from the most general problems for mappings between metric spaces to those connected with fairly concrete and important classes of operators acting in Banach and finite dimensional spaces. Written by a leading expert in the field, the book covers new and powerful techniques, whic...

  18. A generalized Jensen type mapping and its applications

    Directory of Open Access Journals (Sweden)

    Ali Ebadian

    2015-02-01

    Full Text Available Let $X$ and $Y$ be vector spaces. It is shown that a mapping $f : X \\rightarrow Y$ satisfies the functional equation (2d+1 f(\\frac{\\sum_{j=1}^{2d+1} (-1^{j+1} x_j}{2d+1} = \\sum_{j=1}^{2d+1} (-1^{j+1} f(x_j \\end{aligned} if and only if the mapping $f : X \\rightarrow Y$ is additive, and prove the Cauchy-Rassias stability of the functional equation $(0.1$ in Banach modules over a unital $C^*$-algebra, and in Poisson Banach modules over a unital Poisson $C^*$-algebra. Let $A$ and $B$ be unital $C^*$-algebras, Poisson $C^*$-algebras, Poisson $JC^*$-algebras or Lie $JC^*$-algebras. As an application, we show that every almost homomorphism $h : A \\rightarrow B$ is a homomorphism when $h((2d+1^n u y = h((2d+1^n u h(y$ or $h((2d+1^n u \\circ y = h((2d+1^n u\\circ h(y$ for all unitaries $u \\in A$, all $y \\in A$, and $n = 0, 1, 2, \\cdots$, and that every almost linear almost multiplicative mapping $h : A \\rightarrow B$ is a homomorphism when $h((2d+1 x = (2d+1 h(x$ for all $x \\in A$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*$-algebras, Poisson $C^*$-algebras, Poisson $JC^*$-algebras or Lie $JC^*$-algebras, and of Lie $JC^*$-algebra derivations in Lie $JC^*$-algebras.

  19. Space space space

    CERN Document Server

    Trembach, Vera

    2014-01-01

    Space is an introduction to the mysteries of the Universe. Included are Task Cards for independent learning, Journal Word Cards for creative writing, and Hands-On Activities for reinforcing skills in Math and Language Arts. Space is a perfect introduction to further research of the Solar System.

  20. On the convex closed set-valued operators in Banach spaces and their applications in control problems

    International Nuclear Information System (INIS)

    Vu Ngoc Phat; Jong Yeoul Park

    1995-10-01

    The paper studies a class of set-values operators with emphasis on properties of their adjoints and existence of eigenvalues and eigenvectors of infinite-dimensional convex closed set-valued operators. Sufficient conditions for existence of eigenvalues and eigenvectors of set-valued convex closed operators are derived. These conditions specify possible features of control problems. The results are applied to some constrained control problems of infinite-dimensional systems described by discrete-time inclusions whose right-hand-sides are convex closed set- valued functions. (author). 8 refs