The ( Property in Banach Spaces
Directory of Open Access Journals (Sweden)
Danyal Soybaş
2012-01-01
Full Text Available A Banach space is said to have (D property if every bounded linear operator ∶→∗ is weakly compact for every Banach space whose dual does not contain an isomorphic copy of ∞. Studying this property in connection with other geometric properties, we show that every Banach space whose dual has (V∗ property of Pełczyński (and hence every Banach space with (V property has (D property. We show that the space 1( of real functions, which are integrable with respect to a measure with values in a Banach space , has (D property. We give some other results concerning Banach spaces with (D property.
Group representations in Banach spaces and Banach lattices
Wortel, Marten Rogier
2012-01-01
In this thesis, group representations in Banach spaces and Banach lattices are studied. In the first part, chapter 2, a Banach algebra crossed product is constructed, which is an object that allows the translation of group representations in Banach spaces into Banach algebra representations. This
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...
Hytönen, Tuomas; Veraar, Mark; Weis, Lutz
2016-01-01
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...
The Banach-Saks Property of the Banach Product Spaces
Jiang, Zhenglu; Fu, Xiaoyong
2007-01-01
In this paper we first take a detail survey of the study of the Banach-Saks property of Banach spaces and then show the Banach-Saks property of the product spaces generated by a finite number of Banach spaces having the Banach-Saks property. A more general inequality for integrals of a class of composite functions is also given by using this property.
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...
Variational calculus on Banach spaces
International Nuclear Information System (INIS)
Uglanov, A V
2000-01-01
The problem of variational calculus is considered in a (variable) subdomain of a Banach space. Analogues of the basic principles of the finite-dimensional theory are derived: the main formula for variations of a functional, necessary conditions of an extremum, Noether's theorem. All the results obtained are dimension-invariant and become the classical ones in the finite-dimensional setting. The main tool of the analysis is the theory of surface integration in Banach spaces
Spear operators between Banach spaces
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.
Smooth analysis in Banach spaces
Hájek, Petr
2014-01-01
This bookis aboutthe subject of higher smoothness in separable real Banach spaces.It brings together several angles of view on polynomials, both in finite and infinite setting.Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves around two main broad questions: What is the best smoothness of a given Banach space, and its structural consequences? How large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into in
Computable Frames in Computable Banach Spaces
Directory of Open Access Journals (Sweden)
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.
Transitive functions in Banach spaces
Todorov, Vladimir T.; Hamamjiev, Michail A.
2016-12-01
Let X be a real separable Banach algebra and K be a compact subset of X. Denote by C(K) the Banach space of continuous functions from K into X together with the uniform norm topology. We prove in this note that the operator of Gateaux derivative Dh : X → X in direction h ≠ 0 has a cyclic element f0. In other words the forward orbit Ohn(f0):={Dhn(f0)|n =1 ,2 ,⋯} is a dense subset of C(K). Also some other different cases are discussed.
Characterizing R-duality in Banach spaces
DEFF Research Database (Denmark)
Christensen, Ole; Xiao, Xiang Chun; Zhu, Yu Can
2013-01-01
R-duals of certain sequences in Hilbert spaces were introduced by Casazza, Kutyniok and Lammers in 2004 and later generalized to Banach spaces by Xiao and Zhu. In this paper we provide some characterizations of R-dual sequences in Banach spaces.......R-duals of certain sequences in Hilbert spaces were introduced by Casazza, Kutyniok and Lammers in 2004 and later generalized to Banach spaces by Xiao and Zhu. In this paper we provide some characterizations of R-dual sequences in Banach spaces....
Regularization methods in Banach spaces
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
Banach spaces of analytic functions
Hoffman, Kenneth
2007-01-01
A classic of pure mathematics, this advanced graduate-level text explores the intersection of functional analysis and analytic function theory. Close in spirit to abstract harmonic analysis, it is confined to Banach spaces of analytic functions in the unit disc.The author devotes the first four chapters to proofs of classical theorems on boundary values and boundary integral representations of analytic functions in the unit disc, including generalizations to Dirichlet algebras. The fifth chapter contains the factorization theory of Hp functions, a discussion of some partial extensions of the f
The Maslov index in symplectic Banach spaces
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Zhu, Chaofeng
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...
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
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
On Λ-Type Duality of Frames in Banach Spaces
Directory of Open Access Journals (Sweden)
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.
Matrix multiplication operators on Banach function spaces
Indian Academy of Sciences (India)
function spaces and discuss their applications in semigroups for solving the abstract. Cauchy problem. Keywords. Banach function spaces; closed operators; compact operators; Fredholm operators; matrix multiplication operators; semigroups. 1. Introduction. Let ( , , µ) be a σ-finite complete measure space and C be the field ...
Fusion frames and G-frames in Banach spaces
Indian Academy of Sciences (India)
Fusion frames and -frames in Hilbert spaces are generalizations of frames, and frames were extended to Banach spaces. In this article we introduce fusion frames, -frames, Banach -frames in Banach spaces and we show that they share many useful properties with their corresponding notions in Hilbert spaces. We also ...
Banach spaces of continuous functions as dual spaces
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.
Banach spaces that realize minimal fillings
Energy Technology Data Exchange (ETDEWEB)
Bednov, B. B.; Borodin, P. A., E-mail: noriiii@inbox.ru, E-mail: pborodin@inbox.ru [Faculty of Mechanics and Mathematics, Moscow State University (Russian Federation)
2014-04-30
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{sub 1}. The spaces L{sub 1} are characterized in terms of Steiner points (medians). Bibliography: 25 titles. (paper)
Implicit Functions from Topological Vector Spaces to Banach Spaces
Glockner, Helge
2003-01-01
We prove implicit function theorems for mappings on topological vector spaces over valued fields. In the real and complex cases, we obtain implicit function theorems for mappings from arbitrary (not necessarily locally convex) topological vector spaces to Banach spaces.
Observations About the Projective Tensor Product of Banach Spaces
African Journals Online (AJOL)
, 46B, 46E, 47B. Keywords: tensor, Banach, banach space, tensor product, projective norm, greatest crossnorm, semi-embedding, Radon-Nikodym property, absolutely p-summable sequence, strongly p-summable sequence, topological linear ...
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
Restricted uniform boundedness in Banach spaces | Nygaard ...
African Journals Online (AJOL)
Precise conditions for a subset A of a Banach space X are known in order that pointwise bounded on A sequences of bounded linear functionals on X are uniformly bounded. In this paper, we study such conditions under the extra assumption that the functionals belong to a given linear subspace Γ of X*. When Γ = X*, these ...
Matrix multiplication operators on Banach function spaces
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 ...
A characterization of banach spaces containing L.
Rosenthal, H P
1974-06-01
It is proved that a Banach space contains a subspace isomorphic to l(1) if (and only if) it has a bounded sequence with no weak-Cauchy subsequence. The proof yields that a sequence of subsets of a given set has a subsequence that is either convergent or Boolean independent.
Reflexivity on Banach Spaces of Analytic Functions
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B. Yousefi and J. Doroodgar
2008-03-01
Full Text Available . Let X be a Banach space of functions analytic on a plane domain Ω such that for every λ in Ω the functional of evaluation at λ is bounded. Assume further that X contains the constants and admits multiplication by the independent variable z, Mz, as a bounded operator. We give sufficient conditions for Mz to be reflexive.
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.
Distance in Metric Trees and Banach Spaces
Alansari, Monairah
This thesis contains results on metric trees and Banach spaces. There is a common thread which is about distance function. In case of metric trees, special metrics such as radial and river metrics will yield characterization theorems. In the case of Banach spaces we consider the distance from a point in the Banach space to its subspace and by putting conditions on subspaces we obtain results for the speed of convergence of the error of best approximation. We first introduce the concept of metric trees and study some of its properties and provide a new representation of metric trees by using a special set of metric rays, which we called it "crossing point sets". We have captured the four-point condition from these set and shown an equivalence between the metric trees with radial and river metrics, and the crossing point set. As an application of our characterization of metric trees via crossing point sets, we were able to index Brownian motions by a metric tree. Second part of this thesis contains results on the error of best approximation in the context of Banach spaces. The error of the best approximation to x via S is denoted by rho(x,S) defined as follows: rho(x, S) = inf d(x, y) for all y∈S. Note that the well known Weierstrass approximation theorem states that every continuous function defined on a closed interval [a,b] can be uniformly approximated by a polynomial function. Note that the Weierstrass approximation theorem gives no information about the speed of convergence for rho(f, Yn). However, Bernstein Lethargy Theorem (BLT) is about the speed of convergence for rho(f, Y n). We consider a condition on subspaces in order to improve bounds given in the Bernstein's Lethargy Theorem (BLT) for Banach spaces.
Minimization of Tikhonov Functionals in Banach Spaces
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Thomas Bonesky
2008-01-01
Full Text Available Tikhonov functionals are known to be well suited for obtaining regularized solutions of linear operator equations. We analyze two iterative methods for finding the minimizer of norm-based Tikhonov functionals in Banach spaces. One is the steepest descent method, whereby the iterations are directly carried out in the underlying space, and the other one performs iterations in the dual space. We prove strong convergence of both methods.
Extremely strict ideals in Banach spaces
Indian Academy of Sciences (India)
the space of regular Borel measures, it is easy to see that with respect to the projection μ → μ|(0, 1), M is an extremely strict ideal in C([0, 1]) but as the Lebesgue measure is non-atomic, M. ∗. 1 is not the norm closed ..... (Grenoble) 28 (1978) 35–65. [10] Rao T S S R K, On ideals in Banach spaces, Rocky Mountain J. Math.
Three-space problems in Banach space theory
Castillo, Jesús M F
1997-01-01
This book on Banach space theory focuses on what have been called three-space problems. It contains a fairly complete description of ideas, methods, results and counterexamples. It can be considered self-contained, beyond a course in functional analysis and some familiarity with modern Banach space methods. It will be of interest to researchers for its methods and open problems, and to students for the exposition of techniques and examples.
Fusion frames and G-frames in Banach spaces
Indian Academy of Sciences (India)
Amir Khosravi and Behrooz Khosravi. DEFINITION 1.2. Let X be a Banach space with dual space X. ∗ and Xd be a BK-space. A countable family. {gi } in X. ∗ is called an Xd-frame ... In §2 we study g-frames in Banach spaces and in §3 we study fusion frames in Banach spaces. ..... Soc., Providence, RI) (1999). [4] Casazza ...
k-diskcyclic operators on Banach spaces
Bamerni, Nareen; Kılıçman, Adem
2016-06-01
In this paper, we define and study new classes of operators on complex Banach spaces, which we call k-diskcyclic. We use these operators to show that the direct sum of a diskcyclic operator with it self k times (k ≥ 2) does not need to be diskcyclic. However, we show that under certain conditions the latter statement holds true. In particular, we show that an operator T satisfies the diskcyclic criterion if and only if T is k-diskcyclic.
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
Boundedness of biorthogonal systems in Banach spaces
Czech Academy of Sciences Publication Activity Database
Hájek, Petr Pavel; Montesinos, V.
2010-01-01
Roč. 177, č. 1 (2010), s. 145-154 ISSN 0021-2172 R&D Projects: GA ČR GA201/07/0394 Institutional research plan: CEZ:AV0Z10190503 Keywords : M-basis * Banach spaces Subject RIV: BA - General Mathematics Impact factor: 0.630, year: 2010 http://link.springer.com/article/10.1007%2Fs11856-010-0041-x
Topology, isomorphic smoothness and polyhedrality in Banach spaces
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.
Regularization by discretization in Banach spaces
Hämarik, Uno; Kaltenbacher, Barbara; Kangro, Urve; Resmerita, Elena
2016-03-01
We consider ill-posed linear operator equations with operators acting between Banach spaces. For solution approximation, the methods of choice here are projection methods onto finite dimensional subspaces, thus extending existing results from Hilbert space settings. More precisely, general projection methods, the least squares method and the least error method are analyzed. In order to appropriately choose the dimension of the subspace, we consider a priori and a posteriori choices by the discrepancy principle and by the monotone error rule. Analytical considerations and numerical tests are provided for a collocation method applied to a Volterra integral equation in one-dimension space.
Discretization of variational regularization in Banach spaces
International Nuclear Information System (INIS)
Pöschl, Christiane; Resmerita, Elena; Scherzer, Otmar
2010-01-01
Consider a nonlinear ill-posed operator equation F(u) = y, where F is defined on a Banach space X. In this paper we analyze finite-dimensional variational regularization, which takes into account operator approximations and noisy data. As shown in the literature, depending on the setting, convergence of the regularized solutions of the finite-dimensional problems can be with respect to the strong or just a weak topology. In this paper our contribution is twofold. First, we derive convergence rates in terms of Bregman distances in the convex regularization setting under appropriate sourcewise representation of a solution of the equation. Secondly, for particular regularization realizations in nonseparable Banach spaces, we discuss the finite-dimensional approximations of the spaces and the type of convergence, which is needed for the convergence analysis. These considerations lay the fundament for efficient numerical implementation. In particular, we emphasize on the space X of finite total variation functions and analyze in detail the cases when X is the space of the functions of finite bounded deformation and the L ∞ -space. The latter two settings are of interest in numerous problems arising in optimal control, machine learning and engineering
Generalized uniqueness theorem for ordinary differential equations in Banach spaces.
Hassan, Ezzat R; Alhuthali, M Sh; Al-Ghanmi, M M
2014-01-01
We consider nonlinear ordinary differential equations in Banach spaces. Uniqueness criterion for the Cauchy problem is given when any of the standard dissipative-type conditions does apply. A similar scalar result has been studied by Majorana (1991). Useful examples of reflexive Banach spaces whose positive cones have empty interior has been given as well.
Stability for Linear Volterra Difference Equations in Banach Spaces
Directory of Open Access Journals (Sweden)
Rigoberto Medina
2018-01-01
Full Text Available This paper is devoted to studying the existence and stability of implicit Volterra difference equations in Banach spaces. The proofs of our results are carried out by using an appropriate extension of the freezing method to Volterra difference equations in Banach spaces. Besides, sharp explicit stability conditions are derived.
Structure of spectra of linear operators in Banach spaces
International Nuclear Information System (INIS)
Smolyanov, O G; Shkarin, S A
2001-01-01
Descriptive characterizations of the point, the continuous, and the residual spectra of operators in Banach spaces are put forward. In particular, necessary and sufficient conditions for three disjoint subsets of the complex plane to be the point spectrum, the continuous spectrum, and the residual spectrum of a linear continuous operator in a separable Banach space are obtained
Phaseless tomographic inverse scattering in Banach spaces
Estatico, C.; Fedeli, A.; Pastorino, M.; Randazzo, A.; Tavanti, E.
2016-10-01
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 Lp Banach space iterative regularization method which acts on the dual space Lp* . Indeed, it is well known that regularization in special Banach spaces, such us Lp 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.
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)
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 ...
A description of the space of Banach space-valued absolutely p ...
African Journals Online (AJOL)
Abstract. Click on the link to view the abstract. Keywords: Absolutely p-summable sequence, Banach space, Banach lattice, 1-concave operator, sequence space. Quaestiones Mathematicae 31(2008), 101–105 ...
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...... 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....
Approximate Quartic and Quadratic Mappings in Quasi-Banach Spaces
Directory of Open Access Journals (Sweden)
M. Eshaghi Gordji
2011-01-01
Full Text Available we establish the general solution for a mixed type functional equation of aquartic and a quadratic mapping in linear spaces. In addition, we investigate the generalized Hyers-Ulam stability in p-Banach spaces.
Absolute Continuity of Stable Foliations for Mappings of Banach Spaces
Blumenthal, Alex; Young, Lai-Sang
2017-09-01
We prove the absolute continuity of stable foliations for mappings of Banach spaces satisfying conditions consistent with time- t maps of certain classes of dissipative PDEs. This property is crucial for passing information from submanifolds transversal to the stable foliation to the rest of the phase space; it is also used in proofs of ergodicity. Absolute continuity of stable foliations is well known in finite dimensional hyperbolic theory. On Banach spaces, the absence of nice geometric properties poses some additional difficulties.
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 .)
Browder-Krasnoselskii-Type Fixed Point Theorems in Banach Spaces
Directory of Open Access Journals (Sweden)
Taoudi Mohamed-Aziz
2010-01-01
Full Text Available Abstract We present some fixed point theorems for the sum of a weakly-strongly continuous map and a nonexpansive map on a Banach space . Our results cover several earlier works by Edmunds, Reinermann, Singh, and others.
Open problems in the geometry and analysis of Banach spaces
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 ...
Approximate Euler-Lagrange Quadratic Mappings in Fuzzy Banach Spaces
Directory of Open Access Journals (Sweden)
Hark-Mahn Kim
2013-01-01
Full Text Available We consider general solution and the generalized Hyers-Ulam stability of an Euler-Lagrange quadratic functional equation in fuzzy Banach spaces, where , are nonzero rational numbers with , .
Rotundity in transitive and separable Banach spaces | Aizpuru ...
African Journals Online (AJOL)
In every separable Banach space the set of smooth points of the unit ball is a Gδ dense subset of the unit sphere (see [12]). In this paper, we find some conditions in order to obtain a similar result for rotund points. For instance, we prove that if the unit ball of a smooth and separable Banach space is free of rotund points then ...
Higher moments of Banach space valued random variables
Janson, Svante
2015-01-01
The authors define the k:th moment of a Banach space valued random variable as the expectation of its k:th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. The authors study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.
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.
Tauberian theorems for generalized functions with values in Banach spaces
International Nuclear Information System (INIS)
Drozhzhinov, Yu N; Zav'yalov, B I
2002-01-01
We state and prove Tauberian theorems of a new type. In these theorems we give sufficient conditions under which the values of a generalized function (distribution) that are assumed to lie in a locally convex topological space actually belong to some narrower (Banach) space. These conditions are stated in terms of 'general class estimates' for the standard average of this generalized function with a fixed kernel belonging to a space of test functions. The applications of these theorems are based, in particular, on the fact that asymptotical (and some other) properties of the generalized functions under investigation can be described in terms of membership of certain Banach spaces. We apply these theorems to the study of asymptotic properties of solutions of the Cauchy problem for the heat equation in the class of generalized functions of small growth (tempered distributions), and to the study of Banach spaces of Besov-Nikol'skii type
(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
Stability of C0 -quasi semigroups in Banach spaces
Sutrima; Rini Indrati, Ch.; Aryati, Lina
2017-12-01
We concern on the non-autonomous abstract Cauchy problems \\dot{x}=A(t)x(t) on Banach spaces X. If A(t) is the infinitesimal generator of a Co-quasi semigroup R(t, s) on X and x 0 ɛ D, domain of A(t), then the solution of the equation has uniquely representation x(t) = R(0,t)x 0. This representation shows that the stability of the quasi semigroup R(t, s) influences the stability of the solution. In this paper, we investigate the stabilities of C 0-quasi semigroups following the existing theory of stabilities of C 0-semigroups T(t) and bounded evolution operators U(t, s). We devote the uniform, exponential, and strong stability of C 0-quasi semigroups in Banach spaces. The results are applicable for a large class of the time-dependent differential equations with unbounded coefficients in Banach spaces.
DP ∗-Properties of order p on Banach spaces | Fourie | Quaestiones ...
African Journals Online (AJOL)
In this article a new property of Banach spaces, called the DP*-property of order p (briefly denoted by DP* Pp) is introduced and characterisations of Banach spaces with this property and some applications thereof to polynomials and holomorphic functions on Banach spaces are studied. Keywords: Dunford-Pettis property, ...
A strong open mapping theorem for surjections from cones onto Banach spaces
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
A Banach Space Regularization Approach for Multifrequency Microwave Imaging
Directory of Open Access Journals (Sweden)
Claudio Estatico
2016-01-01
Full Text Available A method for microwave imaging of dielectric targets is proposed. It is based on a tomographic approach in which the field scattered by an unknown target (and collected in a proper observation domain is inverted by using an inexact-Newton method developed in Lp Banach spaces. In particular, the extension of the approach to multifrequency data processing is reported. The mathematical formulation of the new method is described and the results of numerical simulations are reported and discussed, analyzing the behavior of the multifrequency processing technique combined with the Banach spaces reconstruction method.
Banach spaces and descriptive set theory selected topics
Dodos, Pandelis
2010-01-01
This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous “intermediate” results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective.
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 equiva...
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
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– ...
A Characterization of Banach Spaces Containing l1
Rosenthal, Haskell P.
1974-01-01
It is proved that a Banach space contains a subspace isomorphic to l1 if (and only if) it has a bounded sequence with no weak-Cauchy subsequence. The proof yields that a sequence of subsets of a given set has a subsequence that is either convergent or Boolean independent. PMID:16592162
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
Smooth approximations of norms in separable Banach spaces
Czech Academy of Sciences Publication Activity Database
Hájek, Petr Pavel; Talponen, J.
2014-01-01
Roč. 65, č. 3 (2014), s. 957-969 ISSN 0033-5606 R&D Projects: GA ČR(CZ) GAP201/11/0345 Institutional support: RVO:67985840 Keywords : Banach space * approximation Subject RIV: BA - General Mathematics Impact factor: 0.640, year: 2014 http://qjmath.oxfordjournals.org/content/65/3/957
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...
Continuous local martingales and stochastic integration in UMD Banach spaces
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
Infimal convolution in Efimov-Stečkin Banach spaces
Czech Academy of Sciences Publication Activity Database
Fabian, Marián
2008-01-01
Roč. 339, č. 1 (2008), s. 735-739 ISSN 0022-247X R&D Projects: GA AV ČR(CZ) IAA100190610 Institutional research plan: CEZ:AV0Z10190503 Keywords : reflexive Banach space * Kadec-Klee norm * infimal convolution Subject RIV: BA - General Mathematics Impact factor: 1.046, year: 2008
A characterization of Banach space with non expansive map
International Nuclear Information System (INIS)
Masaedeh, B. S.; Hadid, S. B.
1996-01-01
In this paper, we characterize a Banach space X with a certain non expansive map T: X → X. We shall prove that T is non expansive if and only if each three dimensional subspace of X has the property that, after rotation by π/2, its unit ball coincides with its dual unit ball. (authors). 3 refs
On weak exponential expansiveness of evolution families in Banach spaces.
Yue, Tian; Song, Xiao-qiu; Li, Dong-qing
2013-01-01
The aim of this paper is to give several characterizations for the property of weak exponential expansiveness for evolution families in Banach spaces. Variants for weak exponential expansiveness of some well-known results in stability theory (Datko (1973), Rolewicz (1986), Ichikawa (1984), and Megan et al. (2003)) are obtained.
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.
On linear isometries of Banach lattices in C0 () C0 () C0 ()-spaces
Indian Academy of Sciences (India)
Consider the space C 0 ( ) endowed with a Banach lattice-norm ‖ ⋅ p ‖ that is not assumed to be the usual spectral norm ‖ ⋅ p ‖ ∞ of the supremum over . A recent extension of the classical Banach-Stone theorem establishes that each surjective linear isometry of the Banach lattice ( C 0 ( ) , ‖ ⋅ p ‖ ) induces ...
Transport equations in weak topologies of dual Banach spaces
International Nuclear Information System (INIS)
Greenberg, W.; Polewczak, J.
1989-01-01
Nonlinear transport equations are studied, in which the nonlinearity, arising from the collision operator, is well behaved in the weak topology of a weakly compactly generated Banach space. The Cauchy problem is posed for general semilinear evolution equations, which can model a variety of diffusion and kinetic equations. Local existence theorems are obtained for such spaces. In particular, the results are applicable to transport equations in L ∞ with appropriate weak (i.e., L 1 ) continuity properties
Borsuk-Ulam theorem in infinite-dimensional Banach spaces
International Nuclear Information System (INIS)
Gel'man, B D
2002-01-01
The well-known classical Borsuk-Ulam theorem has a broad range of applications to various problems. Its generalization to infinite-dimensional spaces runs across substantial difficulties because its statement is essentially finite-dimensional. A result established in the paper is a natural generalization of the Borsuk-Ulam theorem to infinite-dimensional Banach spaces. Applications of this theorem to various problems are discussed
2016-03-13
SECURITY CLASSIFICATION OF: The goal of this project is to fully develop Banach space methods for kernel-based machine learning that extend the Hilbert... space framework of regularized learning. We proposed to study Reproducing Kernel Banach Spaces (RKBS) by the semi-inner-product, develop the theory...Unlimited UU UU UU UU 31-03-2016 1-May-2012 31-Dec-2015 Final Report: Semi-inner-products in Banach Spaces with Applications to Regularized Learning
Geometric properties of Banach spaces and nonlinear iterations
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,...
Singular perturbation method for evolution equations in Banach spaces
International Nuclear Information System (INIS)
Mika, J.
1976-01-01
The singular perturbation method is applied to linear evolution equations in Banach spaces containing a small parameter multiplying the time derivative. Outer and inner asymptotic solutions are formulated and the sense in which they converge to the exact solution is rigorously defined. It is then shown that the sum of the two asymptotic solutions converges uniformly to the exact solution. Possible applications to various physical situations are indicated. (Auth.)
Polynomial algebras and smooth functions in Banach spaces
Czech Academy of Sciences Publication Activity Database
D'Alessandro, Stefania; Hájek, Petr Pavel
2014-01-01
Roč. 266, č. 3 (2014), s. 1627-1646 ISSN 0022-1236 R&D Projects: GA ČR(CZ) GAP201/11/0345; GA MŠk(CZ) 7AMB12FR003 Institutional support: RVO:67985840 Keywords : polynomials in Banach space Subject RIV: BA - General Mathematics Impact factor: 1.322, year: 2014 http://www.sciencedirect.com/science/article/pii/S0022123613004588
S-Mixing Tuple of Operators on Banach Spaces
Directory of Open Access Journals (Sweden)
Wei Wang
2016-01-01
Full Text Available We consider the question: what is the appropriate formulation of Godefroy-Shapiro criterion for tuples of operators? We also introduce a new notion about tuples of operators, S-mixing, which lies between mixing and weakly mixing. We also obtain a sufficient condition to ensure a tuple of operators to be S-mixing. Moreover, we study some new properties of S-mixing operators on several concrete Banach spaces.
Approximating Fixed Points of Generalized Nonexpansive Mappings in Banach Spaces
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Bapurao C. Dhage
2014-10-01
Full Text Available In this paper, we prove a fixed point theorem for the selfmaps of a closed convex and bounded subset of the Banach space satisfying a generalized nonexpansive type condition. Some results concerning the approximations of fixed points with Krasnoselskii and Mann type iterations are also proved under suitable conditions. Our results include the well-known result of Kannan (1968 and Bose and Mukherjee (1981 as the special cases with a different and constructive method.
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
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
A Tannakian Reconstruction Theorem for IndBanach Spaces
Kremnizer, Kobi; Smith, Craig
2017-01-01
Classically, Tannaka-Krein duality allows us to reconstruct a (co)algebra from its category of representation. In this paper we present an approach that allows us to generalise this theory to the setting of Banach spaces. This leads to several interesting applications in the directions of analytic quantum groups, bounded cohomology and galois cohomology. A large portion of this paper is dedicated to such examples.
Margin Error Bounds for Support Vector Machines on Reproducing Kernel Banach Spaces.
Chen, Liangzhi; Zhang, Haizhang
2017-11-01
Support vector machines, which maximize the margin from patterns to the separation hyperplane subject to correct classification, have received remarkable success in machine learning. Margin error bounds based on Hilbert spaces have been introduced in the literature to justify the strategy of maximizing the margin in SVM. Recently, there has been much interest in developing Banach space methods for machine learning. Large margin classification in Banach spaces is a focus of such attempts. In this letter we establish a margin error bound for the SVM on reproducing kernel Banach spaces, thus supplying statistical justification for large-margin classification in Banach spaces.
Greedy Algorithms for Reduced Bases in Banach Spaces
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.
Riesz isomorphisms of tensor products of order unit Banach spaces
Indian Academy of Sciences (India)
Introduction. Let X, Y be compact Hausdorff spaces and E a Banach lattice and F be an abstract. M-space with unit. Let π: C(X, E) → C(Y,F) be a Riesz isomorphism (i.e., order- preserving linear bijection) such that 0 /∈ f (X) if and only if 0 /∈ π(f )(Y ) for each f ∈ C(X, E). Ercan and ¨Onal have proved in [6] that E is Riesz ...
Differentiation Theory over Infinite-Dimensional Banach Spaces
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Claudio Asci
2016-01-01
Full Text Available We study, for any positive integer k and for any subset I of N⁎, the Banach space EI of the bounded real sequences xnn∈I and a measure over RI,B(I that generalizes the k-dimensional Lebesgue one. Moreover, we expose a differentiation theory for the functions defined over this space. The main result of our paper is a change of variables’ formula for the integration of the measurable real functions on RI,B(I. This change of variables is defined by some infinite-dimensional functions with properties that generalize the analogous ones of the standard finite-dimensional diffeomorphisms.
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.
Extremely strict ideals in Banach spaces
Indian Academy of Sciences (India)
Motivated by the notion of an ideal introduced by Godefroy {\\it et al.} ({\\it Studia Math.} {\\bf 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 continuous functions on K is an extremely strict ideal in the space of continuous ...
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 ...
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
Weak and strong solutions for differential equations in Banach spaces
International Nuclear Information System (INIS)
Gomaa, A.M.
2003-01-01
In this paper we give a generalization to recent results by using weak and strong measures of noncompactness. For f:[0,T]xE→E with E is a Banach space we prove that, under suitable assumptions, the Cauchy problem (fd((P) (ar((r((c(x(t)=f(t,x(t)),))(c(t/in R: =set membership[0,T],))))(r((c(x(0)=x 0 ,))(c()))))))) has at least one weak solution furthermore, with certain conditions, the Cauchy problem (P) has a solution. Next under a generalization of the compactness assumptions, we show that (P) has a solution too
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
Stability of interconnected dynamical systems described on Banach spaces
Rasmussen, R. D.; Michel, A. N.
1976-01-01
New stability results for a large class of interconnected dynamical systems (also called composite systems or large scale systems) described on Banach spaces are established. In the present approach, the objective is always the same: to analyze large scale systems in terms of their lower order and simpler subsystems and in terms of their interconnecting structure. The present results provide a systematic procedure of analyzing hybrid dynamical systems (i.e., systems that are described by a mixture of different types of equations). To demonstrate the method of analysis advanced, two specific examples are considered.
International Nuclear Information System (INIS)
Li Zongcheng; Shi Yuming
2009-01-01
This paper is concerned with chaotification of a class of discrete dynamical systems in Banach spaces via the feedback control technique. A chaotification theorem based on heteroclinic cycles connecting repellers for maps in Banach spaces is established. The controlled system is proved to be chaotic in the sense of both Devaney and Li-Yorke. An illustrative example is provided with computer simulations.
Ito's formula in UMD Banach spaces and regularity of solution of the Zakai equation
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
Energy Technology Data Exchange (ETDEWEB)
Li Zongcheng [Department of Mathematics, Shandong Jianzhu University, Jinan, Shandong 250101 (China); Department of Mathematics, Shandong University, Jinan, Shandong 250100 (China)], E-mail: lizongcheng_0905@yahoo.com.cn; Shi Yuming [Department of Mathematics, Shandong University, Jinan, Shandong 250100 (China)], E-mail: ymshi@sdu.edu.cn
2009-11-15
This paper is concerned with chaotification of a class of discrete dynamical systems in Banach spaces via the feedback control technique. A chaotification theorem based on heteroclinic cycles connecting repellers for maps in Banach spaces is established. The controlled system is proved to be chaotic in the sense of both Devaney and Li-Yorke. An illustrative example is provided with computer simulations.
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
Independent functions and the geometry of Banach spaces
Energy Technology Data Exchange (ETDEWEB)
Astashkin, Sergey V; Sukochev, Fedor A
2010-12-31
The main objective of this survey is to present the 'state of the art' of those parts of the theory of independent functions which are related to the geometry of function spaces. The 'size' of a sum of independent functions is estimated in terms of classical moments and also in terms of general symmetric function norms. The exposition is centred on the Rosenthal inequalities and their various generalizations and sharp conditions under which the latter hold. The crucial tool here is the recently developed construction of the Kruglov operator. The survey also provides a number of applications to the geometry of Banach spaces. In particular, variants of the classical Khintchine-Maurey inequalities, isomorphisms between symmetric spaces on a finite interval and on the semi-axis, and a description of the class of symmetric spaces with any sequence of symmetrically and identically distributed independent random variables spanning a Hilbert subspace are considered. Bibliography: 87 titles.
Homomorphisms and functional calculus on algebras on entire functions on Banach spaces
Directory of Open Access Journals (Sweden)
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 $n.$
Stochastic integration in Banach spaces theory and applications
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...
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.
Directory of Open Access Journals (Sweden)
Kim JongKyu
2009-01-01
Full Text Available We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach spaces satisfying some conditions. The results presented in this paper extend and generalize some results concerned with the nonexpansive semigroup in (Chen and He, 2007 and the pseudocontractive mapping in (Zegeye et al., 2007 to the pseudocontractive semigroup in Banach spaces under different conditions.
Incoherent systems and coverings in finite dimensional Banach spaces
Energy Technology Data Exchange (ETDEWEB)
Temlyakov, V N [Steklov Mathematical Institute of the Russian Academy of Sciences (Russian Federation)
2014-05-31
We discuss the construction of coverings of the unit ball of a finite dimensional Banach space. There is a well-known technique based on comparing volumes which gives upper and lower bounds on covering numbers. However, this technique does not provide a method for constructing good coverings. Here we study incoherent systems and apply them to construct good coverings. We use the following strategy. First, we build a good covering using balls with a radius close to one. Second, we iterate this construction to obtain a good covering for any radius. We shall concentrate mainly on the first step of this strategy. Bibliography: 14 titles.
Hilbert asymptotic expansion method for evolution equations in Banach spaces
International Nuclear Information System (INIS)
Mika, J.
1978-01-01
In the paper an abstract initial value problem for a singularly perturbed linear evolution equation in a Banach space is considered. The evolution operator consists of two operators. One of them having an eigenvalue at the origin is multiplied by 1/epsilon where epsilon is a small positive parameter. The Hilbert expansion method is applied to solving the problem and the asymptotic solution is shown to converge uniformly to the exact one with epsilon tending to zero. The results of the paper are applicable to the linear Boltzmann equation if the scattering operator is bounded and the streaming operator is represented in the finite-differnce form. As an example, the Boltzmann equation for neutrons is considered and the Hilbert expansion used to derive the diffusion equation. (author)
Porous sets for mutually nearest points in Banach spaces
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Chong Li
2008-01-01
Full Text Available Let \\(\\mathfrak{B}(X\\ denote the family of all nonempty closed bounded subsets of a real Banach space \\(X\\, endowed with the Hausdorff metric. For \\(E, F \\in \\mathfrak{B}(X\\ we set \\(\\lambda_{EF} = \\inf \\{\\|z - x\\| : x \\in E, z \\in F \\}\\. Let \\(\\mathfrak{D}\\ denote the closure (under the maximum distance of the set of all \\((E, F \\in \\mathfrak{B}(X \\times \\mathfrak{B}(X\\ such that \\(\\lambda_{EF} \\gt 0\\. It is proved that the set of all \\((E, F \\in \\mathfrak{D}\\ for which the minimization problem \\(\\min_{x \\in E, z\\in F}\\|x - z\\|\\ fails to be well posed in a \\(\\sigma\\-porous subset of \\(\\mathfrak{D}\\.
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)
Algorithm for Solving a Generalized Mixed Equilibrium Problem with Perturbation in a Banach Space
Kum Sangho; Yao Jen-Chih; Ceng Lu-Chuan
2010-01-01
Let be a real Banach space with the dual space . Let be a proper functional and let be a bifunction. In this paper, a new concept of -proximal mapping of with respect to is introduced. The existence and Lipschitz continuity of the -proximal mapping of with respect to are proved. By using properties of the -proximal mapping of with respect to , a generalized mixed equilibrium problem with perturbation (for short, GMEPP) is introduced and studied in Banach space . An exis...
Existence of tripled fixed points for a class of condensing operators in Banach spaces.
Karakaya, Vatan; Bouzara, Nour El Houda; Doğan, Kadri; Atalan, Yunus
2014-01-01
We give some results concerning the existence of tripled fixed points for a class of condensing operators in Banach spaces. Further, as an application, we study the existence of solutions for a general system of nonlinear integral equations.
Strong Convergence of a Monotone Projection Algorithm in a Banach Space
Lv, Songtao
2013-01-01
In this paper, a common solution problem is investigated based on a Bregman projection. Strong convergence of the monotone projection algorithm for monotone operators and bifunctions is obtained in a reflexive Banach space. PMID:24348187
Fixed point iterations for a class of nonlinear mappings in certain Banach spaces
International Nuclear Information System (INIS)
Chidume, C.E.
1991-12-01
It is proved that both the Mann iteration method and the Ishikawa iteration method converge strongly, in real Banach spaces with a certain property, to the unique fixed point of nonlinear mappings belonging to class C. 15 refs
Approximating zero points of accretive operators with compact domains in general Banach spaces
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Miyake Hiromichi
2005-01-01
Full Text Available We prove strong convergence theorems of Mann's type and Halpern's type for resolvents of accretive operators with compact domains and apply these results to find fixed points of nonexpansive mappings in Banach spaces.
Some analogies of the Banach contraction principle in fuzzy modular spaces.
Wongkum, Kittipong; Chaipunya, Parin; Kumam, Poom
2013-01-01
We established some theorems under the aim of deriving variants of the Banach contraction principle, using the classes of inner contractions and outer contractions, on the structure of fuzzy modular spaces.
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John R. Graef
2018-02-01
Full Text Available The authors establish sufficient conditions for the existence of solutions to boundary value problems for fractional differential inclusions involving the Hadamard type derivatives of order α ∈ (0,1] in Banach spaces.
The Quest for the Ultimate Anisotropic Banach Space
Baladi, Viviane
2017-02-01
We present a new scale U^{t,s}_p (sBanach spaces, defined via Paley-Littlewood, on which the transfer operator L_g φ = (g \\cdot φ) circ T^{-1} associated to a hyperbolic dynamical system T has good spectral properties. When p=1 and t is an integer, the spaces are analogous to the "geometric" spaces B^{t,|s+t|} considered by Gouëzel and Liverani (Ergod Theory Dyn Syst 26:189-217, 2006). When p>1 and -1+1/pspaces are somewhat analogous to the geometric spaces considered by Demers and Liverani (Trans Am Math Soc 360:4777-4814, 2008). In addition, just like for the "microlocal" spaces defined by Baladi 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.
Restrictive metric regularity and generalized differential calculus in Banach spaces
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Bingwu Wang
2004-10-01
Full Text Available We consider nonlinear mappings f:XÃ¢Â†Â’Y between Banach spaces and study the notion of restrictive metric regularity of f around some point xÃ‚Â¯, 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 xÃ‚Â¯ but its strict derivative Ã¢ÂˆÂ‡f(xÃ‚Â¯ 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.
Spatiality of Derivations of Operator Algebras in Banach Spaces
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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.
Wang, Min
2017-06-01
This paper aims to establish the Tikhonov regularization method for generalized mixed variational inequalities in Banach spaces. For this purpose, we firstly prove a very general existence result for generalized mixed variational inequalities, provided that the mapping involved has the so-called mixed variational inequality property and satisfies a rather weak coercivity condition. Finally, we establish the Tikhonov regularization method for generalized mixed variational inequalities. Our findings extended the results for the generalized variational inequality problem (for short, GVIP( F, K)) in R^n spaces (He in Abstr Appl Anal, 2012) to the generalized mixed variational inequality problem (for short, GMVIP(F,φ , K)) in reflexive Banach spaces. On the other hand, we generalized the corresponding results for the generalized mixed variational inequality problem (for short, GMVIP(F,φ ,K)) in R^n spaces (Fu and He in J Sichuan Norm Univ (Nat Sci) 37:12-17, 2014) to reflexive Banach spaces.
Algorithm for Solving a Generalized Mixed Equilibrium Problem with Perturbation in a Banach Space
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Kum Sangho
2010-01-01
Full Text Available Let be a real Banach space with the dual space . Let be a proper functional and let be a bifunction. In this paper, a new concept of -proximal mapping of with respect to is introduced. The existence and Lipschitz continuity of the -proximal mapping of with respect to are proved. By using properties of the -proximal mapping of with respect to , a generalized mixed equilibrium problem with perturbation (for short, GMEPP is introduced and studied in Banach space . An existence theorem of solutions of the GMEPP is established and a new iterative algorithm for computing approximate solutions of the GMEPP is suggested. The strong convergence criteria of the iterative sequence generated by the new algorithm are established in a uniformly smooth Banach space , and the weak convergence criteria of the iterative sequence generated by this new algorithm are also derived in a Hilbert space.
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
Conical square function estimates in UMD Banach spaces and applications to H?-functional calculi
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
Nonstationary iterated Tikhonov regularization for ill-posed problems in Banach spaces
International Nuclear Information System (INIS)
Jin, Qinian; Stals, Linda
2012-01-01
Nonstationary iterated Tikhonov regularization is an efficient method for solving ill-posed problems in Hilbert spaces. However, this method may not produce good results in some situations since it tends to oversmooth solutions and hence destroy special features such as sparsity and discontinuity. By making use of duality mappings and Bregman distance, we propose an extension of this method to the Banach space setting and establish its convergence. We also present numerical simulations which indicate that the method in Banach space setting can produce better results. (paper)
Periodic and almost periodic solutions for multi-valued differential equations in Banach spaces
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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.
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)
International Nuclear Information System (INIS)
Boivin, A; Paramonov, P V
1998-01-01
For a homogeneous elliptic partial differential operator L with constant coefficients and a class of functions (jet-distributions) defined on a closed, not necessarily compact, subset of R n and belonging locally to a Banach space V, the approximation in the norm of V of functions in this class by entire and meromorphic solutions of the equation Lu=0 is considered. Theorems of Runge, Mergelyan, Roth, and Arakelyan type are established for a wide class of Banach spaces V and operators L they encompass most of the previously considered generalizations of these theorems but also include new results
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)
Conditions for Bounded Closed and Convex Sets to Have a Unique Completion in Banach Spaces
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JI Dong-hai
2017-06-01
Full Text Available In order to study the conditions for bounded closed and convex sets to have a unique completion inreal Banach spaces，known results in this direction are summarized. Based on this，a sufficient condition as well as some necessary and sufficient conditions for bounded closed and convex sets to have a unique completion areprovided. The notion of ( K，u -completeness is extended，and the relation of this notion to the uniqueness of completion in real Banach spaces is discussed.
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J. Tiammee
2017-01-01
Full Text Available In this paper, we prove some fixed point theorems for multivalued nonself G-almost contractions in Banach spaces with a directed graph and give some examples to illustrate our main results. The main results in this paper extend and generalize many known results in the literature therein.
Multiple positive solutions for second order impulsive boundary value problems in Banach spaces
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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.
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)
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
Convergence rates for an iteratively regularized Newton–Landweber iteration in Banach space
International Nuclear Information System (INIS)
Kaltenbacher, Barbara; Tomba, Ivan
2013-01-01
In this paper, we provide convergence and convergence rate results for a Newton-type method with a modified version of Landweber iteration as an inner iteration in a Banach space setting. Numerical experiments illustrate the performance of the method. (paper)
N-th order impulsive integro-differential equations in Banach spaces
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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.
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Gu Feng
2006-01-01
Full Text Available The purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of Chang and Cho (2003, Xu and Ori (2001, and Zhou and Chang (2002.
On the ratios of Arc lengths to chord lengths in real Banach spaces ...
African Journals Online (AJOL)
Two new moduli are introduced to study the ratios of arc lengths to chord lengths in Banach spaces. Basic properties of those two moduli and the relation between them are studied. The relation between those two moduli and some geometric properties, including uniform convexity, uniform nonsquareness, and uniform ...
Positive Solutions for Impulsive Equations of Third Order in Banach Space
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Cai Jingjing
2010-01-01
Full Text Available Using the fixed-point theorem, this paper is devoted to study the multiple and single positive solutions of third-order boundary value problems for impulsive differential equations in ordered Banach spaces. The arguments are based on a specially constructed cone. At last, an example is given to illustrate the main results.
Weakly admissible $\\mathcal{H}_{\\infty}^{-}$-calculus on reflexive Banach spaces
Schwenninger, F.L.; Zwart, Heiko J.
2012-01-01
We show that, given a reflexive Banach space and a generator of an exponentially stable $C_{0}$-semigroup, a weakly admissible operator $g(A)$ can be defined for any $g$ bounded, analytic function on the left half-plane. This yields an (unbounded) functional calculus. The construction uses a
Controllability of impulsive functional differential systems with infinite delay in Banach spaces
International Nuclear Information System (INIS)
Chang Yongkui
2007-01-01
The paper establishes a sufficient condition for the controllability of the first-order impulsive functional differential systems with infinite delay in Banach spaces. We use Schauder's fixed point theorem combined with a strongly continuous operator semigroup. An example is given to illustrate our results
High-frequency asymptotics of solutions of ODE in a Banach space
Sazonov, L. I.
2017-12-01
We construct and justify high-frequency asymptotic expansions of solutions for some class of linear ODE in a Banach space. In particular, we obtain new results in the case when the averaged ODE are degenerate. The author is deceased. The editors are grateful to A. B. Morgulis, who finished the paper after the author’s death.
Approximate Fixed Point Theorems in Banach Spaces with Applications in Game Theory
Brânzei, R.; Morgan, J.; Scalzo, V.; Tijs, S.H.
2002-01-01
In this paper some new approximate fixed point theorems for multifunctions in Banach spaces are presented and a method is developed indicating how to use approximate fixed point theorems in proving the existence of approximate Nash equilibria for non-cooperative games.
Long-standing open problems of Banach space theory: my personal ...
African Journals Online (AJOL)
This attitude is a decisive reason why every mature mathematical theory includes a comprehensive list of challenging problems that are open for a long time, say 25 years. It is the goal of this paper to provide such a list for the theory of Banach spaces. The enumeration of the problems does not indicate any ranking.
Ceng, Lu-Chuan; Lur, Yung-Yih; Wen, Ching-Feng
2017-01-01
The purpose of this paper is to solve the hierarchical variational inequality with the constraint of a general system of variational inequalities in a uniformly convex and 2-uniformly smooth Banach space. We introduce implicit and explicit iterative algorithms which converge strongly to a unique solution of the hierarchical variational inequality problem. Our results improve and extend the corresponding results announced by some authors.
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.
Hyers-Ulam Stability of Jensen Functional Inequality in p-Banach Spaces
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Hark-Mahn Kim
2012-01-01
Full Text Available We prove the Hyers-Ulam stability of the following Jensen functional inequality ∥f((x-y/n+z+f((y-z/n+x+f((z-x/n+y∥≤∥f((x+y+z∥ in p-Banach spaces for any fixed nonzero integer n.
Analysis in Banach spaces volume II probabilistic methods and operator theory
Hytönen, Tuomas; Veraar, Mark; Weis, Lutz
2017-01-01
This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, K-convexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of R-boundedness and Banach space valued square functions developed over the last 20 years. In the last chapter, this content is applied to develop the holomorphic functional calculus of sectorial and bi-sectorial operators in Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to graduate students and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operator-theoretic approac...
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Mouffak Benchohra
2000-03-01
Full Text Available In this paper we investigate the existence of solutions on a compact interval for the first and second order initial-value problems for neutral functional differential and integrodifferential inclusions in Banach spaces. We shall use of a fixed point theorem for condensing maps introduced by Martelli.
Some Results for Integral Inclusions of Volterra Type in Banach Spaces
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Nieto JJ
2010-01-01
Full Text Available We first present several existence results and compactness of solutions set for the following Volterra type integral inclusions of the form: , where , is the infinitesimal generator of an integral resolvent family on a separable Banach space , and is a set-valued map. Then the Filippov's theorem and a Filippov-Ważewski result are proved.
Integral equations of fractional order with multiple time delays in Banach spaces
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Mouffak Benchohra
2012-04-01
Full Text Available In this article, we give sufficient conditions for the existence of solutions for an integral equation of fractional order with multiple time delays in Banach spaces. Our main tool is a fixed point theorem of Monch type associated with measures of noncompactness. Our results are illustrated by an example.
Parametric general variational-like inequality problem in uniformly smooth Banach space
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Kazmi KR
2006-01-01
Full Text Available Using the concept of - -proximal mapping, we study the existence and sensitivity analysis of solution of a parametric general variational-like inequality problem in uniformly smooth Banach space. The approach used may be treated as an extension and unification of approaches for studying sensitivity analysis for various important classes of variational inequalities given by many authors in this direction.
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Yuan George Xian-Zhi
2001-01-01
Full Text Available In this paper, we introduce and study the existence of solutions and convergence of Ishikawa iterative processes with errors for a class of nonlinear variational inclusions with accretive type mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of [4–9, 11, 16–17,19].
On the correct formulation of a nonlinear differential equations in Banach space
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Mahmoud M. El-Borai
2001-01-01
Full Text Available We study, the existence and uniqueness of the initial value problems in a Banach space E for the abstract nonlinear differential equation (dn−1/dtn−1(du/dt+Au=B(tu+f(t,W(t, and consider the correct solution of this problem. We also give an application of the theory of partial differential equations.
The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces
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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.
On linear isometries of Banach lattices in C0( ) C0( ) C0( )-spaces
Indian Academy of Sciences (India)
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidade de. Santiago de Compostela, Spain. E-mail: jm.isidro@usc.es. MS received 22 November 2008; revised 19 January 2009. Abstract. Consider the space C0( ) endowed with a Banach lattice-norm · that is not assumed to be the usual spectral ...
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Xue-song Li
2009-01-01
Full Text Available We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach spaces satisfying some conditions. The results presented in this paper extend and generalize some results concerned with the nonexpansive semigroup in (Chen and He, 2007 and the pseudocontractive mapping in (Zegeye et al., 2007 to the pseudocontractive semigroup in Banach spaces under different conditions.
Weighted Composition Operators Acting on Some Classes of Banach Spaces of Analytic Functions
Hmidouch, Nacir
Let X be a Banach space of analytic functions defined on a domain O contained in the complex plane, upsilon be a fixed analytic function on O and ϕ be an analytic self-map of O. The weighted composition operator is defined on the space H(O) of analytic functions on O by. [special characters omitted]. As specific examples of the operator, we obtain the composition operator Cϕ (upsilon = 1) or the multiplication operator Mupsilon(ϕ( z) = z). [special characters omitted]. The study of weighted composition operators is important because they characterize the isometries of many Banach spaces. In addition, there are interesting connections between the weighted composition operators and Brennan's conjecture, see for example [24] and [25]. Given a weight mu on the open unit disk D, we introduce a one-parameter family of spaces we call iterated weighted-type spaces, [special characters omitted], defined inductively by [special characters omitted]. [special characters omitted]. The special cases n = 0, n = 1, and n = 2 yield the Banach-type spaces, the Blochtype spaces and the Zygmund-type spaces, which have been thoroughly studied by many researchers. In this dissertation, we analyze the Banach space structure of [special characters omitted] for [special characters omitted] . We show that, for n ≥ 3, Vn is an algebra. In addition, we study the weighted composition operators between several iterated weighted-type spaces for [special characters omitted]. Specically, we characterize the bounded, and the compact weighted composition operators, determine operator norm and essential norm estimates, and characterize the invertible weighted composition operators on Vn for n ≠ 2. Moreover, we analyze the weighted composition operators acting between the spaces V3 and V0, V 1 and V2. We determine a necessary and a sufficient condition for a weighted composition operator to be bounded and compact. Furthermore, we conjecture that this condition to be necessary on Vn..
International Nuclear Information System (INIS)
Hein, Torsten
2008-01-01
In this paper we deal with convergence rates for regularizing ill-posed problems with operator mapping from a Hilbert space into a Banach space. Since we cannot transfer the well-established convergence rates theory in Hilbert spaces, only few convergence rates results are known in the literature for this situation. Therefore we present an alternative approach for deriving convergence rates. Hereby we deal with so-called distance functions which quantify the violation of a reference source condition. With the aid of these functions we present error bounds and convergence rates for regularized solutions of linear and nonlinear problems when the reference source condition is not satisfied. We show that the approach of applying distance functions carries over the idea of considering generalized source conditions in Hilbert spaces to inverse problems in Banach spaces in a natural way. Introducing this topic for linear ill-posed problems we additionally show that this theory can be easily extended to nonlinear problems
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)
Miamee, A. G.
1989-01-01
Let B be a Banach space and H and K to Hilbert spaces. The spectral dilation of L(B,H)-valued measures is studied and it is shown that the recent results of Makagon and Salehi (1986) and Rosenberg (1982) on the dilation of L(K,H)-valued measures can be extended to hold for the general Banach space setting of L(B,H)-valued measures. These L(B,H)-valued measures are closely connected to the Banach space valued processes. This connection is recalled and as application of spectral dilation of L(B,H)-valued measures the well known stationary dilation results for scalar valued processes is extended to the case of Banach space valued processes.
Adjoint Subspaces in Banach Spaces, with Applications to Ordinary Differential Subspaces
Coddington, Earl A.; Dijksma, Aalt
1978-01-01
Given two subspaces A0 ⊂ A1 ⊂ W = X ⊕ Y, where X, Y are Banach spaces, we show how to characterize, in terms of generalized boundary conditions, those adjoint pairs A, A* satisfying A0 ⊂ A ⊂ A1, A1* ⊂ A* ⊂ A0* ⊂ W+ = Y* ⊕ X*, where X*, Y* are the conjugate spaces of X, Y, respectively. The
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)
Directory of Open Access Journals (Sweden)
Qinghai He
2013-01-01
Full Text Available In general Banach spaces, we consider a vector optimization problem (SVOP in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra or the union of finitely many generalized polyhedra. Dropping the compactness assumption, we establish some results on structure of the weak Pareto solution set, Pareto solution set, weak Pareto optimal value set, and Pareto optimal value set of (SVOP and on connectedness of Pareto solution set and Pareto optimal value set of (SVOP. In particular, we improved and generalize, Arrow, Barankin, and Blackwell’s classical results in Euclidean spaces and Zheng and Yang’s results in general Banach spaces.
Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces
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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.
A new inequality for the Riemann-Stieltjes integrals driven by irregular signals in Banach spaces.
Łochowski, Rafał M
2018-01-01
We prove an inequality of the Loéve-Young type for the Riemann-Stieltjes integrals driven by irregular signals attaining their values in Banach spaces, and, as a result, we derive a new theorem on the existence of the Riemann-Stieltjes integrals driven by such signals. Also, for any [Formula: see text], we introduce the space of regulated signals [Formula: see text] ([Formula: see text] are real numbers, and W is a Banach space) that may be uniformly approximated with accuracy [Formula: see text] by signals whose total variation is of order [Formula: see text] as [Formula: see text] and prove that they satisfy the assumptions of the theorem. Finally, we derive more exact, rate-independent characterisations of the irregularity of the integrals driven by such signals.
Existence results for differential inclusions with nonlinear growth conditions in Banach spaces.
Bounkhel, Messaoud
2013-01-01
In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, 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 X, I = [0, T], (T > 0), F : I × S → X, is an upper semicontinuous set-valued mapping with convex values satisfying F(t, x) ⊂ c(t)(||x|| + ||x|| (p)K, ∀(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.
Landweber-Kaczmarz method in Banach spaces with inexact inner solvers
Jin, Qinian
2016-10-01
In recent years the Landweber-Kaczmarz method has been proposed for solving nonlinear ill-posed inverse problems in Banach spaces using general convex penalty functions. The implementation of this method involves solving a (nonsmooth) convex minimization problem at each iteration step and the existing theory requires its exact resolution which in general is impossible in practical applications. In this paper we propose a version of the Landweber-Kaczmarz method in Banach spaces in which the minimization problem involved in each iteration step is solved inexactly. Based on the \\varepsilon -subdifferential calculus we give a convergence analysis of our method. Furthermore, using Nesterov's strategy, we propose a possible accelerated version of the Landweber-Kaczmarz method. Numerical results on computed tomography and parameter identification in partial differential equations are provided to support our theoretical results and to demonstrate our accelerated method.
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)
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
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
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.
Weak and Strong Convergence Theorems for Nonexpansive Mappings in Banach Spaces
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Jing Zhao
2008-03-01
Full Text Available The purpose of this paper is to introduce two implicit iteration schemes for approximating fixed points of nonexpansive mapping T and a finite family of nonexpansive mappings {Ti}i=1N, respectively, in Banach spaces and to prove weak and strong convergence theorems. The results presented in this paper improve and extend the corresponding ones of H.-K. Xu and R. Ori, 2001, Z. Opial, 1967, and others.
Mann Type Implicit Iteration Approximation for Multivalued Mappings in Banach Spaces
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Huimin He
2010-01-01
Full Text Available Let K be a nonempty compact convex subset of a uniformly convex Banach space E and let T be a multivalued nonexpansive mapping. For the implicit iterates x0∈K, xn=αnxn-1+(1-αnyn, yn∈Txn, n≥1. We proved that {xn} converges strongly to a fixed point of T under some suitable conditions. Our results extended corresponding ones and revised a gap in the work of Panyanak (2007.
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
Directory of Open Access Journals (Sweden)
Martin Väth
2004-12-01
Full Text Available As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.
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
Directory of Open Access Journals (Sweden)
Suzuki Tomonari
2006-01-01
Full Text Available We prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let be a bounded closed convex subset of a uniformly smooth Banach space . Let be an infinite family of commuting nonexpansive mappings on . Let and be sequences in satisfying for . Fix and define a sequence in by for . Then converges strongly to , where is the unique sunny nonexpansive retraction from onto .
Initial value problem for a class of fractional order inhomogeneous equations in Banach spaces
Fedorov, Vladimir E.; Nazhimov, Roman R.; Gordievskikh, Dmitriy M.
2016-08-01
Initial value problem for a class of fractional order linear inhomogeneous equations in Banach spaces with a bounded operator at the unknown function is considered. The equation contains the Riemann-Liouville fractional derivative and the corresponding initial conditions are set for the fractional derivatives of a solution. The theorem of the problem unique solvability is proved. It is applied for studying of the solvability of initial boundary value problem for a filtration theory equation with Riemann-Liouville time-fractional order.
Uniform ergodicities and perturbation bounds of Markov chains on ordered Banach spaces
Erkursun Özcan, Nazife; Mukhamedov, Farrukh
2017-03-01
In this paper, we consider uniformly mean ergodic and uniformly asymptotical stable Markov operators on ordered Banach spaces. In terms of the ergodicity coefficient, we show the equivalence of uniform and weak mean ergodicities of Markov operators. This result allowed us to establish a category theorem for uniformly mean ergodic Markov operators. Furthermore, using properties of the ergodicity coefficient, we develop the perturbation theory for uniformly asymptotical stable Markov chains in the abstract scheme.
Weak and Strong Convergence Theorems for Nonexpansive Mappings in Banach Spaces
Directory of Open Access Journals (Sweden)
Su Yongfu
2008-01-01
Full Text Available Abstract The purpose of this paper is to introduce two implicit iteration schemes for approximating fixed points of nonexpansive mapping and a finite family of nonexpansive mappings , respectively, in Banach spaces and to prove weak and strong convergence theorems. The results presented in this paper improve and extend the corresponding ones of H.-K. Xu and R. Ori, 2001, Z. Opial, 1967, and others.
On boundary value problems for degenerate differential inclusions in Banach spaces
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Valeri Obukhovskii
2003-01-01
Full Text Available We consider the applications of the theory of condensing set-valued maps, the theory of set-valued linear operators, and the topological degree theory of the existence of mild solutions for a class of degenerate differential inclusions in a reflexive Banach space. Further, these techniques are used to obtain the solvability of general boundary value problems for a given class of inclusions. Some particular cases including periodic problems are considered.
Directory of Open Access Journals (Sweden)
Yong-Kui Chang
2018-02-01
Full Text Available In this article, we establish some new composition theorems on measure pseudo almost automorphic functions via measure theory. The obtained compositions theorems generalize those established under the well-known Lipschitz conditions or the classical uniformly continuous conditions. Then using the theories of resolvent operators and fixed point theorem, we investigate the existence and uniqueness of measure pseudo almost automorphic solutions to a fractional differential equation in Banach spaces.
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 ...
Existence of viable solutions for nonconvex-valued differential inclusions in Banach spaces
International Nuclear Information System (INIS)
Truong Xuan Duc Ha.
1992-07-01
A local existence result is proved for the viability problem dx//dt is an element of F(t,x(t)), x (0) = x0,x(t) is an element of K for all t is an element of [0,a], where F(.,.) is an integrably bounded, (strongly) measurable in t, Lipschitz continuous in x multifunction with closed values and K is a closed subset of a Banach space. (author). 11 refs
Karande, B. D.
2014-12-01
In this paper, we discuss the existence of solutions for a nonlinear functional integral equation of fractional order in R+ via a hybrid fixed point theorem due to B.C. Dhage. This equation will be carried out in the Banach space of real functions defined, continuous and bounded on an unbounded interval R+. Moreover, we show that solutions of this equation are uniformly globally attractive and uniformly globally asymptotically attractive on R+.
On the range of the derivative of Gâteaux-Smooth functions on separable Banach spaces
Czech Academy of Sciences Publication Activity Database
Deville, R.; Hájek, Petr Pavel
2005-01-01
Roč. 145, č. 2 (2005), s. 257-269 ISSN 0021-2172 R&D Projects: GA AV ČR(CZ) IAA1019003; GA AV ČR(CZ) IAA1019205; GA ČR(CZ) GA201/01/1198 Institutional research plan: CEZ:AV0Z10190503 Keywords : Gâteaux-Smooth functions * Banach space * Lipschitz function Subject RIV: BA - General Mathematics Impact factor: 0.448, year: 2005
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 spaces * 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
On omega-limit sets of ordinary differential equations in Banach spaces
Czech Academy of Sciences Publication Activity Database
Hájek, Petr Pavel; Vivi, P.
2010-01-01
Roč. 371, č. 2 (2010), s. 793-812 ISSN 0022-247X R&D Projects: GA AV ČR IAA100190801 Institutional research plan: CEZ:AV0Z10190503 Keywords : omega-limit set * ODE in Banach space Subject RIV: BA - General Mathematics Impact factor: 1.174, year: 2010 http://www. science direct.com/ science /article/pii/S0022247X10004798
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.
Integration over an Infinite-Dimensional Banach Space and Probabilistic Applications
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Claudio Asci
2014-01-01
Full Text Available We study, for some subsets I of N*, the Banach space E of bounded real sequences {xn}n∈I. For any integer k, we introduce a measure over (E,B(E that generalizes the k-dimensional Lebesgue measure; consequently, also a theory of integration is defined. The main result of our paper is a change of variables' formula for the integration.
International Nuclear Information System (INIS)
Semenov, E M; Sukochev, F A
2004-01-01
The properties of the Banach-Saks index are studied in the class of rearrangement invariant spaces. The Banach-Saks indices of the spaces L p,q and some Orlicz spaces are calculated. Generalizations of the Banach-Saks theorems are obtained.
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
Czech Academy of Sciences Publication Activity Database
Kraus, Michal
2015-01-01
Roč. 143, č. 11 (2015), s. 4835-4844 ISSN 0002-9939 R&D Projects: GA ČR(CZ) GAP201/11/0345 Institutional support: RVO:67985840 Keywords : coarse embedding * uniform embedding * quasi- Banach space * Hilbert space Subject RIV: BA - General Mathematics Impact factor: 0.700, year: 2015 http://www.ams.org/journals/proc/2015-143-11/S0002-9939-2015-12626-3/
Convergence rates for the iteratively regularized Gauss–Newton method in Banach spaces
International Nuclear Information System (INIS)
Kaltenbacher, Barbara; Hofmann, Bernd
2010-01-01
In this paper we consider the iteratively regularized Gauss–Newton method (IRGNM) in a Banach space setting and prove optimal convergence rates under approximate source conditions. These are related to the classical concept of source conditions that is available only in Hilbert space. We provide results in the framework of general index functions, which include, e.g. Hölder and logarithmic rates. Concerning the regularization parameters in each Newton step as well as the stopping index, we provide both a priori and a posteriori strategies, the latter being based on the discrepancy principle
Constructive techniques for zeros of monotone mappings in certain Banach spaces.
Diop, C; Sow, T M M; Djitte, N; Chidume, C E
2015-01-01
Let E be a 2-uniformly convex real Banach space with uniformly Gâteaux differentiable norm, and [Formula: see text] its dual space. Let [Formula: see text] be a bounded strongly monotone mapping such that [Formula: see text] For given [Formula: see text] let [Formula: see text] be generated by the algorithm: [Formula: see text]where J is the normalized duality mapping from E into [Formula: see text] and [Formula: see text] is a real sequence in (0, 1) satisfying suitable conditions. Then it is proved that [Formula: see text] converges strongly to the unique point [Formula: see text] Finally, our theorems are applied to the convex minimization problem.
Maximal L2 regularity for Ornstein-Uhlenbeck equation in convex sets of Banach spaces
Cappa, G.
2016-06-01
We study the elliptic equation λu -LΩ u = f in an open convex subset Ω of an infinite dimensional separable Banach space X endowed with a centered non-degenerate Gaussian measure γ, where LΩ is the Ornstein-Uhlenbeck operator. We prove that for λ > 0 and f ∈L2 (Ω , γ) the weak solution u belongs to the Sobolev space W 2 , 2 (Ω , γ). Moreover we prove that u satisfies the Neumann boundary condition in the sense of traces at the boundary of Ω. This is done by finite dimensional approximation.
Flattening Property and the Existence of Global Attractors in Banach Space
Aris, Naimah; Maharani, Sitti; Jusmawati, Massalesse; Nurwahyu, Budi
2018-03-01
This paper analyses the existence of global attractor in infinite dimensional system using flattening property. The earlier stage we show the existence of the global attractor in complete metric space by using concept of the ω-limit compact concept with measure of non-compactness methods. Then we show that the ω-limit compact concept is equivalent with the flattening property in Banach space. If we can prove there exist an absorbing set in the system and the flattening property holds, then the global attractor exist in the system.
Extrapolation of operators acting into quasi-Banach spaces
Lykov, K. V.
2016-01-01
Linear and sublinear operators acting from the scale of L_p spaces to a certain fixed quasinormed space are considered. It is shown how the extrapolation construction proposed by Jawerth and Milman at the end of 1980s can be used to extend a bounded action of an operator from the L_p scale to wider spaces. Theorems are proved which generalize Yano's extrapolation theorem to the case of a quasinormed target space. More precise results are obtained under additional conditions on the quasinorm. Bibliography: 35 titles.
International Nuclear Information System (INIS)
Bredies, Kristian
2009-01-01
We consider the task of computing an approximate minimizer of the sum of a smooth and a non-smooth convex functional, respectively, in Banach space. Motivated by the classical forward–backward splitting method for the subgradients in Hilbert space, we propose a generalization which involves the iterative solution of simpler subproblems. Descent and convergence properties of this new algorithm are studied. Furthermore, the results are applied to the minimization of Tikhonov-functionals associated with linear inverse problems and semi-norm penalization in Banach spaces. With the help of Bregman–Taylor-distance estimates, rates of convergence for the forward–backward splitting procedure are obtained. Examples which demonstrate the applicability are given, in particular, a generalization of the iterative soft-thresholding method by Daubechies, Defrise and De Mol to Banach spaces as well as total-variation-based image restoration in higher dimensions are presented
Riesz isomorphisms of tensor products of order unit Banach spaces
Indian Academy of Sciences (India)
this we recall the Banach–Stone theorem for A(K) spaces, when K is a simplex, due to. Lazar [8]. See [10] for this formulation. We recall that Riesz isomorphism preserves the identity and hence is an isometry. We note that analogous to the continuous function space, multiplication of affine functions on the extreme boundary ...
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
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
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
Ball convergence for Traub-Steffensen like methods in Banach space
Directory of Open Access Journals (Sweden)
Argyros Ioannis K.
2015-12-01
Full Text Available We present a local convergence analysis for two Traub-Steffensen-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. In earlier studies such as [16, 23] Taylor expansions and hypotheses up to the third Fréchet-derivative are used. We expand the applicability of these methods using only hypotheses on the first Fréchet derivative. Moreover, we obtain a radius of convergence and computable error bounds using Lipschitz constants not given before. Numerical examples are also presented in this study.
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
Hanke-Raus heuristic rule for variational regularization in Banach spaces
Jin, Qinian
2016-08-01
We generalize the heuristic parameter choice rule of Hanke-Raus for quadratic regularization to general variational regularization for solving linear as well as nonlinear ill-posed inverse problems in Banach spaces. Under source conditions formulated as variational inequalities, we obtain a posteriori error estimates in term of the Bregman distance. By imposing certain conditions on the random noise, we establish four convergence results; one relies on the source conditions and the other three do not depend on any source conditions. Numerical results are presented to illustrate the performance.
A model of CT dose profiles in Banach space; with applications to CT dosimetry
Weir, Victor J.
2016-07-01
In this paper the scatter component of computed tomography dose profiles is modeled using the solution to a nonlinear ordinary differential equation. This scatter function is summed with a modeled primary function of approximate trapezoidal shape. The primary dose profile is modeled to include the analytic continuation of the Heaviside step function. A mathematical theory is developed in a Banach space. The modeled function is used to accurately fit data from a 256-slice GE Revolution scanner. A 60 cm long body phantom is assembled and used for data collection with both a pencil chamber and a Farmer-type chamber.
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.
On the regularity of mild solutions to complete higher order differential equations on Banach spaces
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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.
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
Local convergence of a fifth convergence order method in Banach space
Directory of Open Access Journals (Sweden)
Ioannis K. Argyros
2017-07-01
Full Text Available We provide a local convergence analysis for a fifth convergence order method to find a solution of a nonlinear equation in a Banach space. In our paper the sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative. Previous works use conditions reaching up to the fourth Fréchet-derivative. This way, the applicability of these methods is extended under weaker conditions and less computational cost for the Lipschitz constants appearing in the convergence analysis. Numerical examples are also given in this paper.
Exponential estimates for stochastic convolutions in 2-smooth Banach spaces
Czech Academy of Sciences Publication Activity Database
Seidler, Jan
2010-01-01
Roč. 15, č. 50 (2010), s. 1556-1573 ISSN 1083-6489 R&D Projects: GA ČR GA201/07/0237 Institutional research plan: CEZ:AV0Z10750506 Keywords : stochastic convolutions in 2-smooth spaces * Burkholder-Davis-Gundy inequality * exponential tail estimates Subject RIV: BA - General Mathematics Impact factor: 0.946, year: 2010 http://library.utia.cas.cz/separaty/2010/SI/seidler-0348352.pdf
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
Kraaij, R.C.
2016-01-01
Let X be a separable metric space and let β be the strict topology on the space of bounded continuous functions on X, which has the space of τ-additive Borel measures as a continuous dual space. We prove a Banach-Dieudonné type result for the space of bounded continuous functions equipped with β:
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)
Directory of Open Access Journals (Sweden)
Jiancai Huang
2012-01-01
Full Text Available We introduce an implicit and explicit iterative schemes for a finite family of nonexpansive semigroups with the Meir-Keeler-type contraction in a Banach space. Then we prove the strong convergence for the implicit and explicit iterative schemes. Our results extend and improve some recent ones in literatures.
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Tian Zhou Xu
2012-01-01
Full Text Available The objective of the present paper is to determine the generalized Hyers-Ulam stability of the mixed additive-cubic functional equation in n-Banach spaces by the direct method. In addition, we show under some suitable conditions that an approximately mixed additive-cubic function can be approximated by a mixed additive and cubic mapping.
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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.
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S. Marshal Anthoni
2004-01-01
Full Text Available We study the existence of mild solutions of the nonlinear second-order neutral functional differential and integrodifferential inclusions with nonlocal conditions in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families of bounded linear operators and a fixed point theorem for condensing maps due to Martelli.
Luo, Ping; Cai, Gang; Shehu, Yekini
2017-01-01
The aim of this paper is to introduce a viscosity iterative algorithm for the implicit midpoint rule of nonexpansive mappings in uniformly smooth spaces. Under some appropriate conditions on the parameters, we prove some strong convergence theorems. As applications, we apply our main results to solving fixed point problems of strict pseudocontractive mappings, variational inequality problems in Banach spaces and equilibrium problems in Hilbert spaces. Finally, we give some numerical examples for supporting our main results.
Nonlinear Stability of ρ-Functional Equations in Latticetic Random Banach Lattice Spaces
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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 .
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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.
Liu, Zhenhai; Migórski, Stanisław; Zeng, Shengda
2017-10-01
In this paper, we firstly introduce a complicated system obtained by mixing a nonlinear evolutionary partial differential equation and a mixed variational inequality in infinite dimensional Banach spaces in the case where the set of constraints is not necessarily bounded and the problem is driven by nonlocal boundary conditions, which is called partial differential variational inequality ((PDVI), for short). Then, we show that the solution set of the mixed variational inequality involved in problem (PDVI) is nonempty, bounded, closed and convex. Moreover, the upper semicontinuity and measurability properties for set-valued mapping U : [ 0 , T ] ×E2 → Cbv (E1) (see (3.7), below) are also established. Finally, several existence results for (PDVI) are obtained by using a fixed point theorem for condensing set-valued operators and theory of measure of noncompactness.
Hybrid methods for accretive variational inequalities involving pseudocontractions in Banach spaces
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Chen Rudong
2011-01-01
Full Text Available Abstract We use strongly pseudocontractions to regularize a class of accretive variational inequalities in Banach spaces, where the accretive operators are complements of pseudocontractions and the solutions are sought in the set of fixed points of another pseudocontraction. In this paper, we consider an implicit scheme that can be used to find a solution of a class of accretive variational inequalities. Our results improve and generalize some recent results of Yao et al. (Fixed Point Theory Appl, doi:10.1155/2011/180534, 2011 and Lu et al. (Nonlinear Anal, 71(3-4, 1032-1041, 2009. 2000 Mathematics subject classification 47H05; 47H09; 65J15
Ezzinbi, Khalil; Ndambomve, Patrice
2016-01-01
In this work, we consider the control system governed by some partial functional integrodifferential equations with finite delay in Banach spaces. We assume that the undelayed part admits a resolvent operator in the sense of Grimmer. Firstly, some suitable conditions are established to guarantee the existence and uniqueness of mild solutions for a broad class of partial functional integrodifferential infinite dimensional control systems. Secondly, it is proved that, under generally mild conditions of cost functional, the associated Lagrange problem has an optimal solution, and that for each optimal solution there is a minimizing sequence of the problem that converges to the optimal solution with respect to the trajectory, the control, and the functional in appropriate topologies. Our results extend and complement many other important results in the literature. Finally, a concrete example of application is given to illustrate the effectiveness of our main results.
Relations between generalized von Neumann-Jordan and James constants for quasi-Banach spaces
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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.
Exponential stability of linear and almost periodic systems on Banach spaces
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Constantin Buse
2003-12-01
Full Text Available Let $v_f(cdot, 0$ the mild solution of the well-posed inhomogeneous Cauchy problem $$ dot v(t=A(tv(t+f(t, quad v(0=0quad tge 0 $$ on a complex Banach space $X$, where $A(cdot$ is an almost periodic (possible unbounded operator-valued function. We prove that $v_f(cdot, 0$ belongs to a suitable subspace of bounded and uniformly continuous functions if and only if for each $xin X$ the solution of the homogeneous Cauchy problem $$ dot u(t=A(tu(t, quad u(0=xquad tge 0 $$ is uniformly exponentially stable. Our approach is based on the spectral theory of evolution semigroups.
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
Cappa, G.; Ferrari, S.
2016-12-01
Let X be a separable Banach space endowed with a non-degenerate centered Gaussian measure μ. The associated Cameron-Martin space is denoted by H. Let ν =e-U μ, where U : X → R is a sufficiently regular convex and continuous function. In this paper we are interested in the W 2 , 2 regularity of the weak solutions of elliptic equations of the type
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)
Boundary Controllability of Integrodifferential Systems in Banach ...
Indian Academy of Sciences (India)
Abstract. Sufficient conditions for boundary controllability of integrodifferential systems in Banach spaces are established. The results are obtained by using the strongly continuous semigroup theory and the Banach contraction principle. Examples are provided to illustrate the theory.
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Zeqing Liu
2006-01-01
Full Text Available We investigate the equivalence between the convergences of the Mann iteration method and the Ishikawa iteration method with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces. A related result deals with the equivalence of the Mann iteration method and the Ishikawa iteration method for φ-pseudocontractive operators in nonempty closed convex subsets of uniformly smooth Banach spaces. The results presented in this paper extend and improve the corresponding results in the literature.
Mixed gradient-Tikhonov methods for solving nonlinear ill-posed problems in Banach spaces
Margotti, Fábio
2016-12-01
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.
Cosso, Andrea; Russo, Francesco
2016-11-01
Functional Itô calculus was introduced in order to expand a functional F(t,Xṡ+t,Xt) depending on time t, past and present values of the process X. Another possibility to expand F(t,Xṡ+t,Xt) consists in considering the path Xṡ+t = {Xx+t,x ∈ [-T, 0]} as an element of the Banach space of continuous functions on C([-T, 0]) and to use Banach space stochastic calculus. The aim of this paper is threefold. (1) To reformulate functional Itô calculus, separating time and past, making use of the regularization procedures which match more naturally the notion of horizontal derivative which is one of the tools of that calculus. (2) To exploit this reformulation in order to discuss the (not obvious) relation between the functional and the Banach space approaches. (3) To study existence and uniqueness of smooth solutions to path-dependent partial differential equations which naturally arise in the study of functional Itô calculus. More precisely, we study a path-dependent equation of Kolmogorov type which is related to the window process of the solution to an Itô stochastic differential equation with path-dependent coefficients. We also study a semilinear version of that equation.
International Nuclear Information System (INIS)
Chidume, C.E.; Bashir, Ali
2007-07-01
Let E be a real uniformly convex Banach space whose dual space E* satisfies the Kadec- Klee property, K be a closed convex nonempty subset of E . Let T 1 , T 2 , . . . , T m : K → K be asymptotically nonexpansive mappings of K into E with sequences (respectively) {k in } n=1 ∞ satisfying k in → 1 as n → ∞, i = 1, 2 , ...,m and Σ n=1 ∞ (k in - 1) in } n=1 ∞ be a sequence in [ε, 1 - ε ], for each i element of { 1, 2 , . . . ,m} (respectively). Let {x n } be a sequence generated for m ≥ 2 by, x 1 element of K, x n+1 = (1 - α 1 n )x n + α 1 n T 1 n y n+m-2 , y n+m-2 = (1 - α 2 n )x n + α 2 n T 2 n y n+m-3 , ..., y n = (1 - α mn )x n + α mn T m n x n , n ≥ 1. Let Intersection i=1 m F (T i ) ≠ 0 . Then, {x n } converges weakly to a common fixed point of the family {T i } i=1 m . Under some appropriate condition on the family {T i } i=1 m , a strong convergence theorem is also roved. (author)
Indian Academy of Sciences (India)
properties of circles, quadrilaterals and polygons. Stefan Banach was judged to have poor eyesight and hence unfit to serve in the military; there- fore, he taught in schools during World War I. In 1916, the senior mathematician Hugo Stein- haus accidentally spotted Banach who was mostly self-taught until then and took him ...
Convergence of hybrid steepest descent method for variational inequalities in Banach spaces
International Nuclear Information System (INIS)
Chidume, C.E.; Chidume, C.O.; Bashir, Ali
2007-07-01
Let E be a real q-uniformly smooth Banach space with constant d q , q ≥ 2. Let T : E → E and G : E → E be a nonexpansive map and an η-strongly accretive map which is also κ - Lipschitzian, respectively. Let {λ n } be a real sequence in [0, 1] satisfying some appropriate conditions. For δ element of (0, ( q η/d q κ q ) q-1 ), define a sequence { x n } iteratively in E by x 0 element of E, x n+1 = T λ n+1 x n = Tx n - δ λ n+1 G(Tx n ), n ≥ 0. Then, {x n } converges strongly to the unique solution x* of the variational inequality problem VI(G,K) (search for x* element of K such that q (y - x*)> ≥ 0 for all y element of K), where K := Fix(T) { x element of E : Tx = x} ≠ 0. A convergence theorem related to fi nite family of nonexpansive maps is also proved. (author)
International Nuclear Information System (INIS)
C.E. Chidume; Bashir, Ali
2007-07-01
Let E be a real reflexive Banach space with uniformly Gateaux differentiable norm. Let K be a nonempty closed convex subset of E. Suppose that every nonempty closed convex bounded subset of K has the fixed point property for nonexpansive mappings. Let T 1 , T 2 , ..., T N be a family of nonexpansive self-mappings of K, with F := intersection i=1 N Fix(T i ) ≠ 0, F = Fix(T N T N-1 ... T 1 ) = Fix(T 1 T N ... T 2 ) = ... Fix(T N-1 T N-2 ... T 1 T N ). Let { λ n } be a sequence in (0, 1) satisfying the following conditions: C1 : lim λ n 0; C2 : Σ λ n = ∞ . For a fixed δ element of (0, 1), define S n : K → K by S n x := (1 - δ )x + δT n x for all x element of K where T n = T n mod N . For arbitrary fixed u, x 0 element of K, let B := { x element of K : T N T N-1 ... T 1 x γx+(1- γ)u, for some γ > 1} be bounded and let the sequence {x n } be defined iteratively by x n+1 λ n+1 u + (1 - λ n+1 )S n+1 x n , for n ≥ 0. Assume that lim n →∞ vertical bar vertical bar T n x n - T n+1 x n vertical bar vertical bar = 0. Then, {x n } converges strongly to a common fixed point of the family T 1 , T 2 , ..., T N . Convergence theorem is also proved for non-self maps. (author)
Some new results for Banach contractions and Edelstein contractive mappings on fuzzy metric spaces
International Nuclear Information System (INIS)
Ciric, Ljubomir
2009-01-01
The main purpose of this paper is to introduce a new class of Banach type fuzzy contractions and to present some fixed and common fixed point theorems for these mappings, as well as for the Edelstein fuzzy locally contractive mappings. Two examples are presented to show that our results are genuine generalizations of many known results.
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Ansari Qamrul Hasan
2006-01-01
Full Text Available We develop an iterative algorithm for computing the approximate solutions of mixed quasi-variational-like inequality problems with skew-symmetric terms in the setting of reflexive Banach spaces. We use Fan-KKM lemma and concept of -cocoercivity of a composition mapping to prove the existence and convergence of approximate solutions to the exact solution of mixed quasi-variational-like inequalities with skew-symmetric terms. Furthermore, we derive the posteriori error estimates for approximate solutions under quite mild conditions.
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Yan Tang
2013-01-01
Full Text Available Suppose that C is a nonempty closed convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. A viscosity iterative process is constructed in this paper. A strong convergence theorem is proved for a common element of the set of fixed points of a finite family of pseudocontractive mappings and the set of solutions of a finite family of monotone mappings. And the common element is the unique solution of certain variational inequality. The results presented in this paper extend most of the results that have been proposed for this class of nonlinear mappings.
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Anantachai Padcharoen
2016-11-01
Full Text Available In this paper, we present a new iterative scheme for finding a common element of the solution set F of the split feasibility problem and the fixed point set F ( T of a right Bregman strongly quasi-nonexpansive mapping T in p-uniformly convex Banach spaces which are also uniformly smooth. We prove strong convergence theorem of the sequences generated by our scheme under some appropriate conditions in real p-uniformly convex and uniformly smooth Banach spaces. Furthermore, we give some examples and applications to illustrate our main results in this paper. Our results extend and improve the recent ones of some others in the literature.
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Zhaoli Ma
2012-01-01
Full Text Available We introduce an iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of fixed points for countable families of total quasi-ϕ-asymptotically nonexpansive mappings in Banach spaces. We prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm in an uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property. The results presented in this paper improve and extend some recent corresponding results.
Xu, Yongchun; Guan, Jinyu; Tang, Yanxia; Su, Yongfu
2018-01-01
We prove some existence theorems for solutions of a certain system of multivariate nonexpansive operator equations and calculate the solutions by using the generalized Mann and Halpern iterative algorithms in uniformly convex and uniformly smooth Banach spaces. The results of this paper improve and extend the previously known ones in the literature.
On the Hausdorff distance and some openings between Banach ...
African Journals Online (AJOL)
... coding of separable Banach spaces as closed subspaces of C(Δ) endowed with the Effros-Borel structure. Also, we discuss the Borel complexity of the Banach-Mazur distance, and we show that its restriction to finite dimensional Banach spaces is Borel. Keywords: Effros-Borel structure, Vietoris topology, Hausdorff metric, ...
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Bekkai Messirdi
2015-03-01
Full Text Available Let X and Y two complex Banach spaces and (A,B a pair of bounded linear operators acting on X with value on Y. This paper is concerned with spectral analysis ofthe pair (A;B: We establish some properties concerning the spectrum of the linear operator pencils (A-lambda B when B is not necessarily invertible and lambda is a complex number. Also, we use the functional calculus for the pair (A,B to prove the corresponding spectral mapping theorem for (A,B. In addition, we define the generalized Kato essential spectrum and the closed range spectra of the pair (A,B and we give some relationships between this spectrums. As application, we describe a spectral analysis of quotient operators.
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
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Jing Zhao
2012-01-01
Full Text Available We introduce an iterative algorithm for finding a common element of the set of common fixed points of a finite family of closed quasi-ϕ-asymptotically nonexpansive mappings, the set of solutions of an equilibrium problem, and the set of solutions of the variational inequality problem for a γ-inverse strongly monotone mapping in Banach spaces. Then we study the strong convergence of the algorithm. Our results improve and extend the corresponding results announced by many others.
Zhong, Min; Wang, Wei
2016-10-01
We extend the globally convergent TIGRA method in Ramlau (2003 Inverse Prob. 19 433-65) for the computation of a minimizer of the Tikhonov-type functional with the p-convex (p≥slant 2) penalty terms Θ for nonlinear forward operators in Banach spaces. The Θ are allowed to be non-smooth to include {L}p-{L}1 or {L}p- TV (total variation) functionals, which are significant in reconstructing special features of solutions such as sparsity and discontinuities. The proposed TIGRA-Θ method uses a dual gradient descent method in the inner iteration and linearly decreases the regularization parameter in the outer iteration. We present the global convergence analysis for the algorithm under suitable parameter selections, and the convergence rate results are provided under both a priori and a posteriori stopping rules. Two numerical examples—an auto-convolution problem and a parameter identification problem—are presented to illustrate the theoretic analysis and verify the effectiveness of the method.
Some Extensions of Banach's Contraction Principle in Complete Cone Metric Spaces
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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.
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
Roughness of (ℤ+, ℤ-)-nonuniform exponential dichotomy for difference equations in Banach spaces.
Lupa, Nicolae
2014-01-01
In this paper we study the roughness of (ℤ+, ℤ-)-nonuniform exponential dichotomy for nonautonomous difference equations in the general context of infinite-dimensional spaces. An explicit form is given for each of the dichotomy constants of the perturbed equation in terms of the original ones. We emphasize that we do not assume any boundedness condition on the coefficients.
Roughness of (ℤ +, ℤ −)-Nonuniform Exponential Dichotomy for Difference Equations in Banach Spaces
2014-01-01
In this paper we study the roughness of (ℤ +, ℤ −)-nonuniform exponential dichotomy for nonautonomous difference equations in the general context of infinite-dimensional spaces. An explicit form is given for each of the dichotomy constants of the perturbed equation in terms of the original ones. We emphasize that we do not assume any boundedness condition on the coefficients. PMID:24592188
Smooth norms and approximation in Banach spaces of the type C (K)
Czech Academy of Sciences Publication Activity Database
Hájek, Petr Pavel; Haydon, R.
2007-01-01
Roč. 58, č. 2 (2007), s. 221-228 ISSN 0033-5606 R&D Projects: GA ČR GA201/04/0090 Institutional research plan: CEZ:AV0Z10190503 Keywords : C(K) space * partitions of unity Subject RIV: BA - General Mathematics Impact factor: 0.612, year: 2007
Stochastic integration in Banach spaces and applications to parabolic evolution equations
Veraar, M.C.
2006-01-01
Stochastic partial differential equations (SPDEs) of evolution type are usually modelled as ordinary stochastic differential equations (SDEs) in an infinite-dimensional state space. In many examples such as the stochastic heat and wave equation, this viewpoint may lead to existence and uniqueness
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
Structure of biprojective Banach algebras with non-trivial radical
International Nuclear Information System (INIS)
Aristov, O Yu
2008-01-01
We study the structure of biprojective Banach algebras. In contrast to earlier results of Selivanov, we admit the presence of nilpotent ideals in the algebras under consideration, and the structure theorem covers almost all known examples. As a corollary, we obtain a complete classification of finite-dimensional biprojective Banach algebras. A major role in the proof is played by the approximation property for certain Banach spaces related to the algebras under consideration
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
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
On the Property of Reflexivity for Multiplication Operators on Banach ...
Indian Academy of Sciences (India)
21
operator Mz are reflexive on a Banach space of functions analytic on a plane domain. AMS Subject Classification: 47B37; 46A25. Keywords: Banach spaces of analytic functions, multiplication operators, reflexive oper- ator, multipliers, Caratheodory hull, bounded point evaluation, spectral set. Introduction. For any set E and ...
The Fatou property in p-convex Banach lattices
Curbera, Guillermo P.; Ricker, Werner J.
2007-04-01
New features of the Banach function space , that is, the space of all [nu]-scalarly pth power integrable functions (with 1[less-than-or-equals, slant]pFatou property plays an essential role and leads to a new representation theorem for a large class of abstract p-convex Banach lattices.
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)
On the extension problem between separable smooth Banach ...
African Journals Online (AJOL)
In this paper, we study the extension of isometric operators between unit spheres of separable smooth Banach spaces with the Radon-Nikodym property (RNP). We show that if there is a surjective isometric operator between unit spheres of separable smooth Banach spaces with RNP, then there exists a codimension one ...
From Hahn-Banach to monotonicity
Simons, Stephen
2008-01-01
In this new edition of LNM 1693 the essential idea is to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a “big convexification” of the graph of the multifunction and the “minimax technique”for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with a generalization of the Hahn-Banach theorem uniting classical functional analysis, minimax theory, Lagrange multiplier theory and convex analysis and culminates in a survey of current results on monotone multifunctions on a Banach space. The first two chapters are aimed at students interested in the development of the basic theorems of functional analysis, which leads painlessly to the theory of minimax theorems, convex Lagrange multiplier theory and convex analysis. The remaining five chapters are useful for those who wish to learn about the current research on monotone multifunctions on (possibly non reflexive) Banach spac...
Aguayo, José; Nova, Miguel; Shamseddine, Khodr
2013-02-01
Let C be the complex Levi-Civita field and let E be a free Banach space over C of countable type. Then E is isometrically isomorphic to c0( {N},C,s) :=leftlbrace (xn)_{nin {N}}:xnin C;lim _{nrArr infty }|xn |s(n)=0rightrbrace, where s:{N}rArr ( 0,infty ) . If the range of s is contained in left|Csetminus leftlbrace 0rightrbrace right|, it is enough to study c0( {N},C ), which will be denoted by c0(C) or, simply, c0. In this paper, we define a natural inner product on c0, which induces the sup-norm of c0. Of course, c0 is not orthomodular, so we characterize those closed subspaces of c0 with an orthonormal complement with respect to this inner product; that is, those closed subspaces M of c0 such that c0 = M ⊕ M⊥. Such a subspace, together with its orthonormal complement, defines a special kind of projection, the so-called normal projection. We present a characterization of such normal projections as well as a characterization of another kind of operators, the compact operators on c0.
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
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.
Banach-stone-like theorems for lattices OF uniformly continuous ...
African Journals Online (AJOL)
New couples of uniform spaces X, Y are found out for which a lattice isomorphism between U(X) and U(Y) implies a uniform homeomorphism between X and Y. Keywords: Banach-Stone, lattice of uniformly continuous functions, R-generated uniform space. Quaestiones Mathematicae 35(2012), 417–430 ...
Moduli and Characteristics of Monotonicity in Some Banach Lattices
Czech Academy of Sciences Publication Activity Database
Foralewski, P.; Hudzik, H.; Kaczmarek, R.; Krbec, Miroslav
-, - (2010), s. 852346 ISSN 1687-1812 R&D Projects: GA AV ČR IAA100190804; GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach lattice * characteristics of monotonicity * Orlicz function space * Orlicz sequence space Subject RIV: BA - General Mathematics http://www.fixedpointtheoryandapplications.com/content/2010/1/852346
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
Morse theory on banach manifolds
International Nuclear Information System (INIS)
Wang, T.
1986-01-01
The Morse Theory of critical points was extended by Palais and Smale to a certain class of functions on Hilbert manifolds. However, there are many variational problems in a nonlinear setting which for technical reasons are posed not on Hilbert but on Banach manifolds of mappings. This paper introduces a concept of a multivalued gradient vector field for a function defined on a Banach manifold. Using this concept, the Morse theory is generalized to some kind of Banach manifolds. The first chapter gives a definition of nondegeneracy of critical points for a real valued function defined on a reflexive Banach manifold, and then a handle-body decomposition theorem and Morse inequalities for this manifold are obtained. The second chapter proves the existence of solutions for a differential inclusion for a so-called accretive multi-valued mapping on a Finsler manifold. The third chapter introduces a definition of nondegeneracy of critical points for a real valued function defined on a general Banach manifold and, furthermore, generalizes the Morse handle-body decomposition theorem and the Morse inequalities to the Banach manifold
El espacio cociente y algunas propiedades geométricas de los espacios de Banach
Directory of Open Access Journals (Sweden)
Jose R. Morales
2009-02-01
Full Text Available We state some geometric properties of Banach spaces, such as uniformly convex spaces, uniformly non-square spaces, local uniformly convex spaces, strictly convex spaces, etc., and we analyze the problem of translating such properties to the quotient space. keywords: uniformly convex sapce, uniformly non-squere sapce, LUR space, (R space.
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 ...
(β) in Banach lattices, Calderón–Lozanowski˘i and Orlicz–Lorentz ...
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
Recall that for any subset C of X, the Kuratowski measure of non-compactness of C is the infimum α(C) of ... Let E = (E, ≤, ·E) be a function Banach lattice over the measure space (T , , µ), where ≤ is the usual ...... [15] Huff R, Banach spaces which are nearly uniformly convex, Rocky Mountain J. Math. 10. (1980) 473–749.
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
Singular symmetric functionals and Banach limits with additional invariance properties
International Nuclear Information System (INIS)
Dodds, P G; Pagter, B de; Sedaev, A A; Semenov, E M; Sukochev, F A
2003-01-01
For symmetric spaces of measurable functions on the real half-line, we study the problem of existence of positive linear functionals monotone with respect to the Hardy-Littlewood semi-ordering, the so-called symmetric functionals. Two new wide classes of symmetric spaces are constructed which are distinct from Marcinkiewicz spaces and for which the set of symmetric functionals is non-empty. We consider a new construction of singular symmetric functionals based on the translation-invariance of Banach limits defined on the space of bounded sequences. We prove the existence of Banach limits invariant under the action of the Hardy operator and all dilation operators. This result is used to establish the stability of the new construction of singular symmetric functionals for an important class of generating sequences
Plongements des espaces métriques dans les espaces de Banach.
Baudier, Florent
2009-01-01
The central theme of this thesis is the embedding of metric spaces into Banach spaces. The embeddings can be different in nature. In this work we mainly focus on coarse, uniform or Lipschitz embeddings. We consider questions about the Lipschitz embedding of various classes of metric spaces, namely locally finite metric spaces or more generally locally finite subsets of Lp-spaces, with 1
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)
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
On property (β) in Banach lattices, Calderón–Lozanowskii and Orlicz ...
Indian Academy of Sciences (India)
The geometry of Calderón–Lozanowskiĭ spaces, which are strongly connected with the interpolation theory, was essentially developing during the last few years (see [4, 9, 10, 12, 13, 17]). On the other hand many authors investigated property () in Banach spaces (see [7, 19, 20, 21, 25, 26]). The first aim of this paper is to ...
Tikhonov regularization in Banach spaces—improved convergence rates results
International Nuclear Information System (INIS)
Hein, Torsten
2009-01-01
In this paper, we deal with convergence rates for a Tikhonov-like regularization approach for linear ill-posed problems in Banach spaces. Here, we deal with the so-called distance functions which quantify the violation of an introduced reference source condition. Under validity of this reference source condition we derive convergence rates which are well-known as optimal in a Hilbert space situation. Additionally, we present error bounds and convergence rates which are based on the decay rate of the distance functions when the reference source condition is violated
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].
Directory of Open Access Journals (Sweden)
Kazimierz Włodarczyk
2015-01-01
Full Text Available Let C={Cα}α∈A∈[1;∞A, A-index set. A quasi-triangular space (X,PC;A is a set X with family PC;A={pα:X2→[0,∞, α∈A} satisfying ∀α∈A ∀u,v,w∈X {pα(u,w≤Cα[pα(u,v+pα(v,w]}. For any PC;A, a left (right family JC;A generated by PC;A is defined to be JC;A={Jα:X2→[0,∞, α∈A}, where ∀α∈A ∀u,v,w∈X {Jα(u,w≤Cα[Jα(u,v+Jα(v,w]} and furthermore the property ∀α∈A {limm→∞pα(wm,um=0} (∀α∈A {limm→∞pα(um,wm=0} holds whenever two sequences (um:m∈N and (wm:m∈N in X satisfy ∀α∈A {limm→∞supn>mJα(um,un=0 and limm→∞Jα(wm,um=0} (∀α∈A {limm→∞supn>mJα(un,um=0 and limm→∞Jα(um,wm=0}. In (X,PC;A, using the left (right families JC;A generated by PC;A (PC;A is a special case of JC;A, we construct three types of Pompeiu-Hausdorff left (right quasi-distances on 2X; for each type we construct of left (right set-valued quasi-contraction T:X→2X, and we prove the convergence, existence, and periodic point theorem for such quasi-contractions. We also construct two types of left (right single-valued quasi-contractions T:X→X and we prove the convergence, existence, approximation, uniqueness, periodic point, and fixed point theorem for such quasi-contractions. (X,PC;A generalize ultra quasi-triangular and partiall quasi-triangular spaces (in particular, generalize metric, ultra metric, quasi-metric, ultra quasi-metric, b-metric, partial metric, partial b-metric, pseudometric, quasi-pseudometric, ultra quasi-pseudometric, partial quasi-pseudometric, topological, uniform, quasi-uniform, gauge, ultra gauge, partial gauge, quasi-gauge, ultra quasi-gauge, and partial quasi-gauge spaces.
Banach Gelfand Triples for Applications in Physics and Engineering
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
The Dual space of an asymmetric normed linear space | Garcia-Raffi ...
African Journals Online (AJOL)
semilinear space and prove that it is a biBanach space if Y is so. Mathematics Subject Classification (2000): 46B10, 54E50, 54E15, 54H99. Key words: Asymmetric normed linear space; semilinear space; continuous linear mapping; dual space; bidual space; biBanach space; quasi-metric; weak* topology; compactness.
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.
On Peano's theorem in Banach spaces
Czech Academy of Sciences Publication Activity Database
Hájek, Petr Pavel; Johanis, M.
2010-01-01
Roč. 249, č. 12 (2010), s. 3342-3351 ISSN 0022-0396 R&D Projects: GA AV ČR IAA100190801 Institutional research plan: CEZ:AV0Z10190503 Keywords : diferential equations Subject RIV: BA - General Mathematics Impact factor: 1.261, year: 2010 http://www.sciencedirect.com/science/article/pii/S0022039610003505
Trichotomy for dynamical systems in Banach spaces.
Stoica, Codruţa
2013-01-01
We construct a framework for the study of dynamical systems that describe phenomena from physics and engineering in infinite dimensions and whose state evolution is set out by skew-evolution semiflows. Therefore, we introduce the concept of ω-trichotomy. Characterizations in a uniform setting are proved, using techniques from the domain of nonautonomous evolution equations with unbounded coefficients, and connections with the classic notion of trichotomy are given. The statements are sustained by several examples.
Uniformly convex functions on Banach spaces
Czech Academy of Sciences Publication Activity Database
Borwein, J.; Guirao, A. J.; Hájek, Petr Pavel; Vanderwerff, J.
2009-01-01
Roč. 137, č. 3 (2009), s. 1081-1091 ISSN 0002-9939 R&D Projects: GA AV ČR IAA100190502; GA AV ČR IAA100190801 Institutional research plan: CEZ:AV0Z10190503 Keywords : power type 2 * uniform convexity Subject RIV: BA - General Mathematics Impact factor: 0.640, year: 2009
Odd Degree Polynomials on Real Banach Spaces
Czech Academy of Sciences Publication Activity Database
Aron, R. M.; Hájek, Petr Pavel
2007-01-01
Roč. 11, č. 1 (2007), s. 143-153 ISSN 1385-1292 R&D Projects: GA AV ČR IAA100190502; GA ČR GA201/04/0090 Institutional research plan: CEZ:AV0Z10190503 Keywords : odd degree polynomials * zero sets Subject RIV: BA - General Mathematics Impact factor: 0.356, year: 2007
Regularity of difference equations on Banach spaces
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.
Spectral theory of linear operators and spectral systems in Banach algebras
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...
Homomorphisms of certain Banach function algebras
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
. } < ∞ is denoted by Lipα(X, d). These algebras are called Lipschitz algebras of order α and were first studied by Sherbert. The Lipschitz algebras Lipα(X, d) for α ≤ 1 are natural. Banach function algebras on X under the norm f α = f X + pα(f ) ...
Very smooth points of spaces of operators
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
ball has a very smooth point then the space has the Radon–Nikodým property. We give an example of a smooth Banach space without any very smooth points. Keywords. Very smooth points; spaces of operators; M-ideals. 1. Introduction. A Banach space X is said to be very smooth if every unit vector has a unique norming.
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 $A$
A G.N.S.-type theorem for a non-involutive Banach algebra
International Nuclear Information System (INIS)
Desquith, E.
1991-02-01
Given an involutive Banach algebra A with a bounded approximate identity, the elegant construction by Gelfand, Naimark and Segal, associates to each positive linear functional f on A, a triple (H f , π f , ξ f ), where H f is a Hilbert space with scalar product denoted by: , π f is a representation of A into L(H f ), the space of bounded linear operators on H f , ξ f is a cyclic vector in H f , such that: f(x)= f (x)ξ f , ξ f >, for all x is an element of A. In this result, the existence of a (multiplicative) involution on A, is central. The aim of this paper is to show that such a construction may be performed for a non-involutive Banach algebra, to obtain a similar triple (H, ω, ξ) as above. Moreover, this procedure indeed enables us to associate to the topological dual of any Banach space, a liminary C*-subalgebra of L(H). A notion of compact Hilbert algebras will be introduced, together with a method of construction of a large collection of such spaces. (author). 14 refs
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...
Geometric properties on non-complete spaces
African Journals Online (AJOL)
complete normed spaces. We show the existence of a non-rotund Banach space with a rotund dense maximal subspace. As a consequence, we prove that every separable Banach space can be renormed to be non-rotund and to contain a dense ...
Sifat Aljabar Banach Komutatif dan Elemen Identitas pada Kelas D(K
Directory of Open Access Journals (Sweden)
Malahayati Malahayati
2013-11-01
Full Text Available The first Baire class of bounded functions on separable metric spaces K denoted by B1(k. One of the most important subclass of B1(k is D(K, by D(K is denoted the class of all functions on K which are differences of bounded semicontinuous functions. In this paper we proved that D(K is abelian Banach algebra and identity element
Chistyakov, VV
2005-01-01
It is shown that the space of functions of n real variables with finite total variation in the sense of Vitali, Hardy and Krause, defined on a rectangle I-a(b) C R-n, is a Banach algebra under the pointwise operations and Hildebrandt-Leonov's norm. This result generalizes the classical case of
(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 ...
(2n − 1)-Ideal amenability of triangular banach algebras
Indian Academy of Sciences (India)
2Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran. ∗Corresponding author. E-mail: sina.etemad@azaruniv.ac.ir; etefagh@iaut.ac.ir; minaettefagh@gmail.com. MS received 29 May 2013; revised 14 June 2014. Abstract. Let A and B be two unital Banach algebras and let M be an unital Banach.
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
Choquet and Shilov Boundaries, Peak Sets, and Peak Points for Real Banach Function Algebras
Directory of Open Access Journals (Sweden)
Davood Alimohammadi
2013-01-01
Full Text Available Let be a compact Hausdorff space and let be a topological involution on . In 1988, Kulkarni and Arundhathi studied Choquet and Shilov boundaries for real uniform function algebras on . Then in 2000, Kulkarni and Limaye studied the concept of boundaries and Choquet sets for uniformly closed real subspaces and subalgebras of or . In 1971, Dales obtained some properties of peak sets and p-sets for complex Banach function algebras on . Later in 1990, Arundhathi presented some results on peak sets for real uniform function algebras on . In this paper, while we present a brief account of the work of others, we extend some of their results, either to real subspaces of or to real Banach function algebras on .
Modern methods in topological vector spaces
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
Comments on some recent generalization of the Banach contraction principle
Directory of Open Access Journals (Sweden)
Tomonari Suzuki
2016-04-01
Full Text Available Abstract We study Browder and CJM contractions of integral type. As a result, we give an alternative proof of some recent generalization of the Banach contraction principle by Jleli and Samet.
Functional Analysis: Entering Hilbert Space
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard
In the second edition, I have expanded the material on normed vector spaces and their operators presented in Chapter 1 to include proofs of the Open Map-ping Theorem, the Closed Graph Theorem and the Hahn-Banach The orem. The material on operators between normed vector spaces is further expanded...... in a new chapter on Fredholm theory (Chapter 6). Fredholm theory originates in pioneering work of the Swedish mathematician Erik Ivar Fred-holm on integral equations, which inspired the study of a new class of bounded linear operators, known as Fredholm operators. Chapter 6 presents the basic elements...... of the theory of Fredholm operators on general Banach spaces, not only on Hilbert spaces, since this is important for applications of the theory. The more general setting with Banach spaces requires that we develop the theory of dual operators between Banach spaces to replace the use of adjoint operators...
Annihilators in infinite-dimensional Grassmann-Banach algebras
International Nuclear Information System (INIS)
Ivashchuk, V.D.
1989-01-01
A family of infinite-dimensional Grassmann-Banach algebras over a complete normed field K is considered. It is shown that every element G of the family is an associative supercommutative Banach superalgebra over K: G double-bond G 0 circle-plus G 1 with zero annihilators G 0 perpendicular double-bond G 1 perpendicular double-bond(G 1 (κ) ) perpendicular double-bond(0), k ≥ 2
Lower bounds for homological dimensions of Banach algebras
International Nuclear Information System (INIS)
Selivanov, Yurii V
2007-01-01
Let A be a commutative unital Banach algebra with infinite spectrum. Then by Helemskii's global dimension theorem the global homological dimension of A is strictly greater than one. This estimate has no analogue for abstract algebras or non-normable topological algebras. It is proved in the present paper that for every unital Banach algebra B the global homological dimensions and the homological bidimensions of the Banach algebras A widehat-otimes B and B (assuming certain restrictions on A) are related by A widehat-otimes B≥2 + dg B and A widehat-otimes B≥2 + db B. Thus, a partial extension of Helemskii's theorem to tensor products is obtained. Bibliography: 28 titles.
On approximation of flat Banach modules by free modules
International Nuclear Information System (INIS)
Aristov, O Yu
2005-01-01
The local structure of flat Banach modules is considered; in particular, it is shown that if a flat module has the approximation property, then it is freely approximable, that is, the identity operator on it is approximated by operators each of which admits factorization through a free Banach module satisfying a natural finiteness condition. Among the maps involved in the factorization, the first is approximately multiplicative up to ε on compact sets, and the second is exactly a morphism of modules. The properties of freely approximable and approximately projective modules are studied. It is proved that the standard complex for calculating the derived functor Ext is locally asymptotically exact in the first term for an arbitrary second argument if and only if its first argument is a flat Banach module.
Derivations into duals of ideals of Banach algebras
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
(ii) An ideally amenable Banach algebra is weakly amenable. Let A# be the unitization of the commutative Banach algebra A. Then for each closed two-sided ideal I of A consider the following short exact sequence. ( ): 0 −→ K ı. −→ A#ˆ⊗I π. −→ I −→ 0, where π is given by π(a ⊗ i) = ai for all a ∈ A#, i ∈ I, ı is the embedding ...
Winning the pressing down game but not Banach Mazur
Kellner, Jakob; Pauna, Matti; Shelah, Saharon
2006-01-01
Let $S$ be the set of those $\\alpha\\in\\omega_2$ that have cofinality $\\omega_1$. It is consistent relative to a measurable that the nonempty player wins the pressing down game of length $\\omega_1$, but not the Banach Mazur game of length $\\omega+1$ (both games starting with $S$).
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 ...
polynomially peripheral range-preserving maps between Banach ...
Indian Academy of Sciences (India)
11
[1] J. Araujo, J. J. Font, On Silov boundaries for subspaces of continuous functions ,. Topology Appl. 77 (1997), 79-85. [2] H. G. Dales, Boundaries and peak points for Banach function algebras, Proc. London. Math. Soc. 22 (1971), 121-136. [3] O. Hatori, T. Miura and H. Takagi, Characterization of the isometric isomorphisms.
polynomially peripheral range-preserving maps between Banach ...
Indian Academy of Sciences (India)
11
The study of maps between Banach algebras which preserves some structures such as the norm, the spectrum, the range ... case where c = ab and they characterize the general form of a surjection T between two uniform algebras A and B which ..... |S f|≤|Sg| on ∂(B). The converse statement can be proved in a similar way.
Functional Analysis: Entering Hilbert Space
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard
In the second edition, I have expanded the material on normed vector spaces and their operators presented in Chapter 1 to include proofs of the Open Map-ping Theorem, the Closed Graph Theorem and the Hahn-Banach The orem. The material on operators between normed vector spaces is further expanded ...... of the new material on normed vector spaces and their operators, the book can hopefully serve as a general introduction to functional analysis viewed as a theory of infinite dimensional linear spaces and linear operators acting on them.......In the second edition, I have expanded the material on normed vector spaces and their operators presented in Chapter 1 to include proofs of the Open Map-ping Theorem, the Closed Graph Theorem and the Hahn-Banach The orem. The material on operators between normed vector spaces is further expanded...... of the theory of Fredholm operators on general Banach spaces, not only on Hilbert spaces, since this is important for applications of the theory. The more general setting with Banach spaces requires that we develop the theory of dual operators between Banach spaces to replace the use of adjoint operators...
Nuclearity for dual operator spaces
Indian Academy of Sciences (India)
spaces. This result is used to prove that V. ∗∗ is nuclear if and only if V is nuclear and. V. ∗∗ is exact. Keywords. Operator space; nuclear; injective. 1. Introduction. The theory of operator spaces is a recently arising area in modern analysis, which is a natural non-commutative quantization of Banach space theory.
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), ...
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 .
Representations of weak and strong integrals in banach spaces.
Brooks, J K
1969-06-01
We establish a representation of the Gelfand-Pettis (weak) integral in terms of unconditionally convergent series. Moreover, absolute convergence of the series is a necessary and sufficient condition in order that the weak integral coincide with the Bochner integral. Two applications of the representation are given. The first is a simplified proof of the countable additivity and absolute continuity of the indefinite weak integral. The second application is to probability theory; we characterize the conditional expectation of a weakly integrable function.
Tools for analysis of Dirac structures on banach spaces
Iftime, Orest V.; Sandovici, Adrian; Golo, Goran
2005-01-01
Power-conserving and Dirac structures are known as an approach to mathematical modeling of physical engineering systems. In this paper connections between Dirac structures and well known tools from standard functional analysis are presented. The analysis can be seen as a possible starting framework
Stochastic antiderivational equations on non-Archimedean Banach spaces
Directory of Open Access Journals (Sweden)
S. V. Ludkovsky
2003-01-01
non-Archimedean fields are investigated. Theorems about existence and uniqueness of the solutions are proved under definite conditions. In particular, Wiener processes are considered in relation to the non-Archimedean analog of the Gaussian measure.
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
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
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
STABILITY OF A FUNCTIONAL EQUATION IN COMPLEX BANACH SPACES
PRATAP MONDAL; T.K. SAMANTA
2016-01-01
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 ) .
Stability of stationary and periodic solutions equations in Banach space
Directory of Open Access Journals (Sweden)
A. Ya. Dorogovtsev
1997-01-01
Full Text Available Linear difference and differential equations with operator coefficients and random stationary (periodic input are considered. Conditions are presented for the mean stability of stationary (periodic solutions under small perturbation of the coefficients.
Uniqueness for stochastic evolution equations in Banach spaces
Czech Academy of Sciences Publication Activity Database
Ondreját, Martin
2004-01-01
Roč. 426, - (2004), s. 1-63 ISSN 0012-3862 R&D Projects: GA ČR GA201/01/1197 Institutional research plan: CEZ:AV0Z1019905 Keywords : Yamada * Watanabe theory for SPDE Subject RIV: BA - General Mathematics
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
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. science direct.com/ science /article/pii/S0022247X17309186?via%3Dihub
The Socle and finite dimensionality of some Banach algebras
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
It follows that µ = 0. By Proposition 1, we have Soc(L1(G)) = Soc(M(G)). In the following Theorem we will provide some conditions on A and A∗∗ that are sufficient to guarantee finite dimensionality. Theorem 1. Let A be a Banach algebra with a bounded approximate identity. If. Soc(A∗∗) = A∗∗. , then A is finite dimensional.
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.
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
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. science direct.com/ science /article/pii/S0024379517305761?via%3Dihub
Indian Academy of Sciences (India)
The space C[0,1] is also not reflexive. One of the nice consequences of the Riesz representation theorem is that every Hilbert space is reflexive. 5. Vector Valued Integration. Let us consider the unit interval [0,1] endowed with the Lebesgue- measure. Let V be a normed linear space over R. Let ϕ : [0,1] →. V be a continuous ...
Lectures given at the Banach Center and C.I.M.E. Joint Summer School
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.
Convergence Rates in the Law of Large Numbers for Arrays of Banach Valued Martingale Differences
Directory of Open Access Journals (Sweden)
Shunli Hao
2013-01-01
Full Text Available We study the convergence rates in the law of large numbers for arrays of Banach valued martingale differences. Under a simple moment condition, we show sufficient conditions about the complete convergence for arrays of Banach valued martingale differences; we also give a criterion about the convergence for arrays of Banach valued martingale differences. In the special case where the array of Banach valued martingale differences is the sequence of independent and identically distributed real valued random variables, our result contains the theorems of Hsu-Robbins-Erdös (1947, 1949, and 1950, Spitzer (1956, and Baum and Katz (1965. In the real valued single martingale case, it generalizes the results of Alsmeyer (1990. The consideration of Banach valued martingale arrays (rather than a Banach valued single martingale makes the results very adapted in the study of weighted sums of identically distributed Banach valued random variables, for which we prove new theorems about the rates of convergence in the law of large numbers. The results are established in a more general setting for sums of infinite many Banach valued martingale differences. The obtained results improve and extend those of Ghosal and Chandra (1998.
Indian Academy of Sciences (India)
in elliptic problems connected to homogenization, control theory and isoperimetric .... multiplication by reals only and consider X as a real normed lin- ear space, then g is a continuous linear ..... same operator in R3. Fundamental solutions have several uses; they can be used to solve partial differential equations using the ...
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 ...
Functional Analysis: Entering Hilbert Space
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard
In the second edition, I have expanded the material on normed vector spaces and their operators presented in Chapter 1 to include proofs of the Open Map-ping Theorem, the Closed Graph Theorem and the Hahn-Banach The orem. The material on operators between normed vector spaces is further expanded ...
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.
Inequalities of Čebyšev Type for Lipschitzian Functions in Banach Algebras
Directory of Open Access Journals (Sweden)
Boldea Marius V.
2016-12-01
Full Text Available In this paper we give some Čebyšev type norm inequalities for two Lipschitzian functions on Banach algebras. Some examples for power function, exponential and the resolvent functions are also provided
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2006-03-01
Full Text Available In this paper, we prove an existence theorem for hyperbolic differential equations in Banach algebras under Lipschitz and Caratheodory conditions. The existence of extremal solutions is also proved under certain monotonicity conditions.
Directory of Open Access Journals (Sweden)
Bapurao Dhage
2005-11-01
Full Text Available In this paper some existence theorems for the first order differential equations in Banach algebras is proved under the mixed generalized Lipschitz, Carathéodory and monotonicity conditions.
Variedades invariantes de puntos fijos hiperbólicos en espacios de Banach
Mamani Cayani, Juan Mesias; Mamani Cayani, Juan Mesias
1999-01-01
El presente trabajo de investigación, generaliza las Propiedades de las Variedades Invariantes de Punto Fijos Hiperbólicos en Espacios Vectoriales de Dimensión Finita a Espacios de Dimensión Infinita Espacios de Banach, utilizando para ello argumentos de Análisis Funcional y Teoría de Variedades diferenciables modelados en Espacios de Banach Tesis
On Zweier Sequence Spaces and de la Vall\\'{e}e-Poussin mean of order $\\alpha$
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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 $[\\mathcal{Z}_{\\lambda}^{\\alpha}]_{\\infty}(p.$
-Metric Space: A Generalization
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Farshid Khojasteh
2013-01-01
Full Text Available We introduce the notion of -metric as a generalization of a metric by replacing the triangle inequality with a more generalized inequality. We investigate the topology of the spaces induced by a -metric and present some essential properties of it. Further, we give characterization of well-known fixed point theorems, such as the Banach and Caristi types in the context of such spaces.
A note on regular martingales in Riesz spaces | Korostenski ...
African Journals Online (AJOL)
... setting of Riesz spaces. The aim of this note is to show that the space of such martingales is a Riesz space. We derive an analogue of a result of Troitsky's on regular norm bounded martingales in Banach lattices. Keywords: filtration; martingale; submartingale; Riesz space. Quaestiones Mathematicae 31(2008), 219–224 ...
The β-dual of the Cesàro sequence spaces defined on a generalized Orlicz space
Haryadi; Supama; Zulijanto, Atok
2017-10-01
In this paper we characterized the β-dual of the Cesàro sequence space with terms in a generalized Orlicz space. Further, we find that the dual is a generalization of the dual of the Cesàro space in the classical Banach space Lp for1 < p < ∞.
Nice surjections on spaces of operators
Indian Academy of Sciences (India)
A bounded linear operator is said to be nice if its adjoint preserves extreme points of the dual unit ball. Motivated by a description due to Labuschagne and Mascioni [9] of such maps for the space of compact operators on a Hilbert space, in this article we consider a description of nice surjections on K ( X , Y ) for Banach ...
Directory of Open Access Journals (Sweden)
Park Choonkil
2007-01-01
Full Text Available We prove the Hyers-Ulam-Rassias stability of homomorphisms in real Banach algebras and of generalized derivations on real Banach algebras for the following Cauchy-Jensen functional equations: , , which were introduced and investigated by Baak (2006. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper (1978.
Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras
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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.
On some interpolation properties in locally convex spaces
Energy Technology Data Exchange (ETDEWEB)
Pater, Flavius [Department of Mathematics, Politehnica University of Timişoara, 300004 Timişoara (Romania)
2015-03-10
The aim of this paper is to introduce the notion of interpolation between locally convex spaces, the real method, and to present some elementary results in this setting. This represents a generalization from the Banach spaces framework to the locally convex spaces sequentially complete one, where the operators acting on them are locally bounded.
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.
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
A contribution to group representations in locally convex spaces
International Nuclear Information System (INIS)
Jurzak, J.P.
1977-01-01
Let U be a continuous representation of a (connected) locally compact group G in a separated locally convex space E. It is shown that the study of U is equivalent to the study of a family Usub(i) of continuous representations of G in Frechet spaces Fsub(i). If U is equicontinuous, the Fsub(i) are Banach spaces, and the Usub(i) are realized by isomeric operators. When U is topologically irreducible, it is Naemark equivalent to a Frechet (or isomeric Banach, in the equicontinuous case) continuous representation. Similar results hold for semi-groups. (Auth.)
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
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.
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)
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
Cox, S.G.
2012-01-01
The thesis deals with various aspects of the study of stochastic partial differential equations driven by Gaussian noise. The approach taken is functional analytic rather than probabilistic: the stochastic partial differential equation is interpreted as an ordinary stochastic differential equation
Functional equations in matrix normed spaces
Indian Academy of Sciences (India)
Cauchy additive functional equation is said to be an additive mapping. Hyers [19] gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers' theorem was generalized by Aoki [2] for additive mappings and by Rassias [37] for linear map- pings by considering an unbounded Cauchy difference.
Some structural properties of vector valued φ-function sequence space
Gultom, S. N. R.; Herawati, E.
2018-01-01
The sequence space W(M), where M is an Orlicz function was introduced by Parashar and Choudhary [1] and Maddox [2]. Let f be φ-function and X be a Banach space. In this work, we introduce vector valued sequence space defined by f, denoted by W(X, f). We study some topological properties and inclusion relations of this space.
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).
Caristi Fixed Point Theorem in Metric Spaces with a Graph
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M. R. Alfuraidan
2014-01-01
Full Text Available We discuss Caristi’s fixed point theorem for mappings defined on a metric space endowed with a graph. This work should be seen as a generalization of the classical Caristi’s fixed point theorem. It extends some recent works on the extension of Banach contraction principle to metric spaces with graph.
Operator Ideal of Cesaro Type Sequence Spaces Involving Lacunary Sequence
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Awad A. Bakery
2014-01-01
Full Text Available The aim of this paper is to give the sufficient conditions on the sequence space Cesθ,p defined in Lim (1977 such that the class of all bounded linear operators between any arbitrary Banach spaces with nth approximation numbers of the bounded linear operators in Cesθ,p form an operator ideal.
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
When L1 of a vector measure is an AL-space
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...
Partial inner product spaces theory and applications
Antoine, Jean-Pierre
2009-01-01
Partial Inner Product (PIP) Spaces are ubiquitous, e.g. Rigged Hilbert spaces, chains of Hilbert or Banach spaces (such as the Lebesgue spaces Lp over the real line), etc. In fact, most functional spaces used in (quantum) physics and in signal processing are of this type. The book contains a systematic analysis of PIP spaces and operators defined on them. Numerous examples are described in detail and a large bibliography is provided. Finally, the last chapters cover the many applications of PIP spaces in physics and in signal/image processing, respectively. As such, the book will be useful both for researchers in mathematics and practitioners of these disciplines.
Functions with bounded variation in locally convex space
Duchoň, Miloslav; Debiève, Camille
2011-01-01
The present paper is concerned with some properties of functions with values in locally convex vector space, namely functions having bounded variation and generalizations of some theorems for functions with values in locally convex vector spaces replacing Banach spaces, namely Theorem: If X is a sequentially complete locally convex vector space, then the function x(·): [a, b] → X having a bounded variation on the interval [a, b] defines a vector-valued measure m on borelian subsets of [a, b] ...
Proximinal subspaces of finite codimension in direct sum spaces
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
d(x, A)}. Proximinal subspaces of finite codimension have been studied by various authors (see. [1–4, 7–10]). In this paper we obtain a necessary and sufficient condition for proximinality of subspaces of finite codimension inc0-direct sum of Banach spaces in terms of the proxim- inality of the corresponding subspaces of ...
Quasicontraction Mappings in Modular Spaces without Δ2-Condition
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Khamsi MA
2008-01-01
Full Text Available Abstract As a generalization to Banach contraction principle, Ćirić introduced the concept of quasi-contraction mappings. In this paper, we investigate these kinds of mappings in modular function spaces without the -condition. In particular, we prove the existence of fixed points and discuss their uniqueness.
UG-differentiability entails Hahn-Banach | Morillon | Quaestiones ...
African Journals Online (AJOL)
Denoting by ACN the countable axiom of choice, we show in ZF+ACN that the dual ball of a uniformly G^ateaux-differentiable normed space is compact in the weak* topology. In ZF, we prove that this dual ball is (closely) convex-compact in the weak* topology. We deduce that uniformly G^ateaux–differentiable normed ...
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
Decay estimate of global solutions to the generalized double dispersion model in Morrey spaces
Wang, Yu-Zhu; Gu, Liuxin; Wang, Yinxia
2017-08-01
In this paper, we investigate the initial value problem for the generalized double dispersion model in Morrey spaces. Based on the decay properties of the solution operator in Morrey spaces, global existence and decay estimates of solutions are proved by Banach fixed point theorem.
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
On existence of extremal solutions of nonlinear functional integral equations in Banach algebras
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B. C. Dhage
2004-01-01
Full Text Available An algebraic fixed point theorem involving the three operators in a Banach algebra is proved using the properties of cones and they are further applied to a certain nonlinear integral equations of mixed type x(t=k(t,x(μ(t+[f(t,x(θ(t](q(t+∫0σ(tv(t,sg(s,x(η(sds for proving the existence of maximal and minimal solutions. Our results include the earlier fixed point theorems of Dhage (1992 and 1999 as special cases with a different but simple method.
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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.
Sunder, V S
2016-01-01
The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the reader to the basic facts concerning the various von Neumann–Schatten ideals, the compact operators, the trace-class operators and all bounded operators. .
A Randomized Gossip Consenus Algorithm on Convex Metric Spaces
2012-01-01
Property (C) are not that rare. Indeed, by Smulian’s Theorem ([3], page 443), every weakly compact convex subset of a Banach space has Property (C...www.isr.umd.edu A randomized gossip consensus algorithm on convex metric spaces Ion Matei, Christoforos Somarakis, John S. Baras ISR TECHNICAL REPORT 2012-02...2. REPORT TYPE 3. DATES COVERED 00-00-2012 to 00-00-2012 4. TITLE AND SUBTITLE A randomized gossip consensus algorithm on convex metric spaces
Isometric Reflection Vectors and Characterizations of Hilbert Spaces
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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.
Fixed Points of Multivalued Maps in Modular Function Spaces
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Kutbi MarwanA
2009-01-01
Full Text Available The purpose of this paper is to study the existence of fixed points for contractive-type and nonexpansive-type multivalued maps in the setting of modular function spaces. We also discuss the concept of -modular function and prove fixed point results for weakly-modular contractive maps in modular function spaces. These results extend several similar results proved in metric and Banach spaces settings.
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Mabrouk Bragdi
2013-01-01
Full Text Available We discuss the existence of solutions for a class of some separated boundary differential inclusions of fractional orders 2<α<3 involving the Caputo derivative. In order to obtain necessary conditions for the existence result, we apply the fixed point technique, fractional calculus, and multivalued analysis.
Compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions
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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.
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.
On different results for new three step iteration process in Banach spaces.
Ullah, Kifayat; Arshad, Muhammad
2016-01-01
In this paper we propose a new iteration process, called AK iteration process, for approximation of fixed points for contraction mappings. We show that our iteration process is faster than the leading Vatan Two-step iteration process for contraction mappings. Numerical examples are given to support the analytic proofs. Stability of AK iteration process and data dependence result for contraction mappings by employing AK iteration process are also discussed.
On Polynomial Stability of Variational Nonautonomous Difference Equations in Banach Spaces
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Mihail Megan
2013-01-01
Full Text Available Our goal in this paper is to give characterizations for some concepts of polynomial stability for variational nonautonomous difference equations. The obtained results can be considered generalizations for the case of variational nonautonomous difference equations of some theorems proved by Barbashin (1967, Datko (1973, and Lyapunov (1992, for evolution operators.
Chidume, C E; Bello, A U; Usman, B
2015-01-01
Let [Formula: see text], [Formula: see text], and [Formula: see text] be a strongly monotone and Lipschitz mapping. A Krasnoselskii-type sequence is constructed and proved to converge strongly to the unique solution of [Formula: see text]. Furthermore, our technique of proo f is of independent interest.
Weak solutions for nonlinear fractional differential equations on reflexive Banach spaces
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Mouffak Benchohra
2010-09-01
Full Text Available The aim of this paper is to investigate a class of boundary value problem for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.
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
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, ...
An Existence Result for Nonlinear Fractional Differential Equations on Banach Spaces
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Djamila Seba
2009-01-01
Full Text Available The aim of this paper is to investigate a class of boundary value problem for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of noncompactness.
Directory of Open Access Journals (Sweden)
Mouffak Benchohra
2012-01-01
Full Text Available The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.
On the mild solutions of higher-order differential equations in Banach spaces
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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.
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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 \
Integral representations of cylindrical local martingales in every separable Banach space
Czech Academy of Sciences Publication Activity Database
Ondreját, Martin
2007-01-01
Roč. 10, č. 3 (2007), s. 1-15 ISSN 0219-0257 R&D Projects: GA ČR GA201/04/0750 Institutional research plan: CEZ:AV0Z10190503 Keywords : brownian representation Subject RIV: BA - General Mathematics Impact factor: 0.689, year: 2007
Exact Filling of Figures with the Derivatives of Smooth Mappings Between Banach Spaces
Czech Academy of Sciences Publication Activity Database
Azagra, D.; Fabian, Marián; Jiménez-Sevilla, M.
2005-01-01
Roč. 48, č. 4 (2005), s. 481-499 ISSN 0008-4395 R&D Projects: GA AV ČR(CZ) IAA1019003; GA ČR(CZ) GA201/01/1198 Institutional research plan: CEZ:AV0Z10190503 Keywords : n-times smooth * Fréchet smooth * Gateaux smooth bump Subject RIV: BA - General Mathematics Impact factor: 0.316, year: 2005
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
International Nuclear Information System (INIS)
Smirnov, V A; Kuznetsova, S V; Mayorova, I V
1998-01-01
We consider the following problem: how can one apply the methods employed for describing the cohomology of algebras and based on the use of the A ∞ -structures of Stasheff to describe the cohomology of Banach algebras and locally convex algebras
Chistyakov, VV
2005-01-01
We characterize superposition Nemytskii operators, which map the Banach algebra of functions of n real variables with finite total variation in the sense of Vitali, Hardy and Krause into itself and satisfy the global Lipschitz condition. Our results extend previous results in this direction by
Very smooth points of spaces of operators
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Our notation and terminology is standard and can be found in [HWW]. For a Banach space X by ∂eX1 we denote the set of extreme points. 2. Very smooth points. Let M ⊂ X be a closed subspace. It was observed in [MR] that if x ∈ M is a smooth point of X then it is a smooth point of M. It is easy to see that if every continuous.
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
Sobolev spaces associated to the harmonic oscillator
Indian Academy of Sciences (India)
of Hermite functions is dense in any of them (Proposition 1). .... PROPOSITION 1. Let p be in the range 1
Banach space. Moreover, the sets # and C. ∞ c are dense in Wk,p. Proof. To see that W1,p is ...... By the mean value theorem, the first integral of the last expression can be written as.
Toeplitz Operators, Pseudo-Homogeneous Symbols, and Moment Maps on the Complex Projective Space
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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.
Fixed Points, Inner Product Spaces, and Functional Equations
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Park Choonkil
2010-01-01
Full Text Available Rassias introduced the following equality , , for a fixed integer . Let be real vector spaces. It is shown that, if a mapping satisfies the following functional equation for all with , which is defined by the above equality, then the mapping is realized as the sum of an additive mapping and a quadratic mapping. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the above functional equation in real Banach spaces.
Composition operators between Bloch type spaces and Zygmund ...
Indian Academy of Sciences (India)
can be identified with the Lipschitz space Lip. 1−α consisting of holomorphic functions f on. Bn such that. | f (z) − f (w)| ≤ C|z − w|1−α for all z,w ∈ Bn (see [6]). Therefore, for a function f ∈ Z, it may extend continuously to the closed unit ball Bn. Suppose that (X, ·X ) is a Banach space of holomorphic functions on Bn satisfying.
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 spaces * compact metric-spaces * approximation properties Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.375, year: 2016 https://projecteuclid.org/euclid.bbms/1503453711
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
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)
Czech Academy of Sciences Publication Activity Database
Gogatishvili, Amiran; Neves, J. S.; Opic, B.
2011-01-01
Roč. 30, č. 1 (2011), s. 1-27 ISSN 0232-2064 R&D Projects: GA ČR GA201/08/0383 Institutional research plan: CEZ:AV0Z10190503 Keywords : Bessel potentials * Sobolev-type spaces * rearrangement-invariant Banach function spaces Subject RIV: BA - General Mathematics Impact factor: 0.327, year: 2011 http://www.ems-ph.org/journals/show_abstract.php?issn=0232-2064&vol=30&iss=1&rank=1
Indian Academy of Sciences (India)
. They married in September 1920. Their son Stefan Jr. ... second-order memory prevents him from repeating himself too often before the same public!” The group of mathematicians at Lwów also established in 1929, the journal Studia Mathe-.
A coincidence point result in Menger spaces using a control function
Energy Technology Data Exchange (ETDEWEB)
Choudhury, Binayak S. [Department of Mathematics, Bengal Engineering and Science University, P.O. B. Garden, Shibpur, Howrah, West Bengal 711103 (India); Das, Krishnapada [Department of Mathematics, Bengal Engineering and Science University, P.O. B. Garden, Shibpur, Howrah, West Bengal 711103 (India)], E-mail: kestapm@yahoo.co.in
2009-12-15
In the present work we prove a coincidence point theorem in Menger spaces with a t-norm T which satisfies the condition sup{l_brace}T(t,t):t<1{r_brace}=1. As a corollary of our theorem we obtain some existing results in metric spaces and probabilistic metric spaces. Particularly our result implies a probabilistic generalization of Banach contraction mapping theorem. We also support our result by an example.
Optimal embeddings and compact embeddings of Bessel-potential-type spaces
Czech Academy of Sciences Publication Activity Database
Gogatishvili, Amiran; Neves, J. S.; Opic, Bohumír
2009-01-01
Roč. 262, č. 3 (2009), s. 645-682 ISSN 0025-5874 R&D Projects: GA ČR GA201/05/2033 Institutional research plan: CEZ:AV0Z10190503 Keywords : Bessel-potential-type spaces * generalized Hölder spaces * rearrangement invariant Banach function spaces Subject RIV: BA - General Mathematics Impact factor: 0.895, year: 2009
Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces
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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∥=supz∈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.
The Spaces of Functions of Two Variables of Bounded κΦ-Variation in the Sense of Schramm-Korenblum
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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.
On Monotone Generalized Quasi contraction mappings in modular metric spaces with a graph
Directory of Open Access Journals (Sweden)
Habtu Zegeye
2017-12-01
Full Text Available One of the most popular result in Mathematics is the Banach Contraction principle in a complete metric space. Due to its wide range of applications, many mathematicians generalized the Banach contraction principle in different directions. One of the generalizations is due to Jachymski [Proc.Am. Math. Soc. 1(136,1359-1373], in which he considered a complete metric space with a graph structure. Alfraidan [Fixed Point Theory and Applications (2015 2015:93. doi 10.1186/s13663-015-0341-2] generalized the work of Jachymski for quasi-contraction mappings in both metric and modular metric spaces with a graph structure. Modular metric spaces are more general than the usual metric spaces. In this paper, we extend Alfraidan's result to a generalized quasi contraction mappings.
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
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/
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
Composition operators on function spaces
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...
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 CJh 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 CJh acting from normal weighted Bloch spaces to QT,S spaces. The related sufficient and necessary conditions are given.
Uniqueness of a pre-generator for $C_0$-semigroup on a general locally convex vector space
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.
On the moduli and characteristic of monotonicity in Orlicz-Lorentz function spaces
Czech Academy of Sciences Publication Activity Database
Foralewski, P.; Hudzik, H.; Kaczmarek, R.; Krbec, Miroslav; Wojtowicz, M.
2013-01-01
Roč. 20, č. 4 (2013), s. 955-970 ISSN 0944-6532 R&D Projects: GA ČR GAP201/10/1920 Institutional research plan: CEZ:AV0Z10190503 Keywords : Kothe space * Banach lattice * Orlicz-Lorentz space Subject RIV: BA - General Mathematics Impact factor: 0.592, year: 2013 http://www.heldermann.de/JCA/JCA20/JCA204/jca20052.htm
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
Variable Lebesgue spaces and hyperbolic systems
2014-01-01
This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function space properties of variable Lebesgue spaces; proofs are modeled on the classical theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such as convolution operators and singular integrals. The text is mostly self-contained, with only some mor...
Caballero, Josefa; Darwish, Mohamed Abdalla; Sadarangani, Kishin
2014-01-01
We study the existence of solutions for the following fractional hybrid boundary value problem $$ \\begin{cases} \\displaystyle D_{0^+}^{\\alpha}\\bigg[\\frac{x(t)}{f(t,x(t))}\\bigg]+g(t,x(t))=0, &0< t< 1,\\\\ x(0)=x(1)=0, \\end{cases} $$ where $1< \\alpha\\leq 2$ and $D_{0^+}^{\\alpha}$ denotes the Riemann-Liouville fractional derivative. The main tool is our study is the technique of measures of noncompactness in the Banach algebras. Some examples are presented to il...
Elements of mathematics topological vector spaces
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).
Functional differential equations with unbounded delay in extrapolation spaces
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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.
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...... it is demonstrated that they can be extended to a class of polynomially bounded smooth functions allowing a realization of the full Hopf algebra structure on κ -Minkowski space. Furthermore, we give an explicit realization of the action of the κ -Poincaré algebra as an involutive Hopf algebra on this representation...
Elements of Hilbert spaces and operator theory
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...
Global Attractivity Results for Mixed-Monotone Mappings in Partially Ordered Complete Metric Spaces
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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.
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.
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A.M. Gomaa
2012-07-01
(Qx·(t∈A(tx(t+Fd(t,θtx,t∈[0,T],x=C,on[-d,0], where Fd : [0,T] × CE([−d,0] → Pfc(E, Pfc(E is the set of all nonempty closed convex subsets of E while θt : CE([−d,t] → CE([−d,0] defined by θtx(s = x(t + s ∀ x ∈ CE([−d,t], ∀s ∈ [−d,0] and {A(t : 0 ⩽ t ⩽ b} is a family of densely defined closed linear operators generating a continuous evolution operator S(t,s.
Czech Academy of Sciences Publication Activity Database
Ondreját, Martin
2005-01-01
Roč. 55, č. 4 (2005), s. 1003-1039 ISSN 0011-4642 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : Brownian representations * martingale problem * strong Markov property Subject RIV: BA - General Mathematics Impact factor: 0.112, year: 2005
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.
Differential calculus in normed linear spaces
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...
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.
Additive subgroups of topological vector spaces
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.
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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.
Fixed point theory in metric type spaces
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...
Interpolation functors and interpolation spaces
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...
Effective representations of the space of linear bounded operators
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Vasco Brattka
2003-04-01
Full Text Available Representations of topological spaces by infinite sequences of symbols are used in computable analysis to describe computations in topological spaces with the help of Turing machines. From the computer science point of view such representations can be considered as data structures of topological spaces. Formally, a representation of a topological space is a surjective mapping from Cantor space onto the corresponding space. Typically, one is interested in admissible, i.e. topologically well-behaved representations which are continuous and characterized by a certain maximality condition. We discuss a number of representations of the space of linear bounded operators on a Banach space. Since the operator norm topology of the operator space is nonseparable in typical cases, the operator space cannot be represented admissibly with respect to this topology. However, other topologies, like the compact open topology and the Fell topology (on the operator graph give rise to a number of promising representations of operator spaces which can partially replace the operator norm topology. These representations reflect the information which is included in certain data structures for operators, such as programs or enumerations of graphs. We investigate the sublattice of these representations with respect to continuous and computable reducibility. Certain additional conditions, such as finite dimensionality, let some classes of representations collapse, and thus, change the corresponding graph. Altogether, a precise picture of possible data structures for operator spaces and their mutual relation can be drawn.
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
Convergence theorems for a class of nonlinear 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 be a mapping of K into itself and suppose T is an element of C (in the notation of Browder and Petryshyn; and Rhoades). It is proved that each of two well known fixed point iteration methods (the Mann and the Ishikawa iteration methods) converges strongly to the unique fixed point of T. (author). 20 refs
Quantitative Embeddability and Connectivity in Metric Spaces
Eriksson-Bique, Sylvester David
This thesis studies three analytic and quantitative questions on doubling metric (measure) spaces. These results are largely independent and will be presented in separate chapters. The first question concerns representing metric spaces arising from complete Riemannian manifolds in Euclidean space. More precisely, we find bi-Lipschitz embeddings ƒ for subsets A of complete Riemannian manifolds M of dimension n, where N could depend on a bound on the curvature and diameter of A. The main difficulty here is to control the distortion of such embeddings in terms of the curvature of the manifold. In constructing the embeddings, we will study the collapsing theory of manifolds in detail and at multiple scales. Similar techniques give embeddings for subsets of complete Riemannian orbifolds and quotient metric spaces. The second part of the thesis answers a question about finding quantitative and weak conditions that ensure large families of rectifiable curves connecting pairs of points. These families of rectifiable curves are quantified in terms of Poincare inequalities. We identify a new quantitative connectivity condition in terms of curve fragments, which is equivalent to possessing a Poincare inequality with some exponent. The connectivity condition arises naturally in three different contexts, and we present methods to find Poincare inequalities for the spaces involved. In particular, we prove such inequalities for spaces with weak curvature bounds and thus resolve a question of Tapio Rajala. In the final part of the thesis we study the local geometry of spaces admitting differentiation of Lipschitz functions with certain Banach space targets. The main result shows that such spaces can be characterized in terms of Poincare inequalities and doubling conditions. In fact, such spaces can be covered by countably many pieces, each of which is an isometric subset of a doubling metric measure space admitting a Poincare inequality. In proving this, we will find a new way to
Geraghty Type Generalized F-Contractions and Related Applications in Partial b-Metric Spaces
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Deepak Singh
2017-01-01
Full Text Available The purpose of this paper is to introduce new concepts of (α,β-admissible Geraghty type generalized F-contraction and to prove that some fixed point results for such mappings are in the perspective of partial b-metric space. As an application, we inaugurate new fixed point results for Geraghty type generalized graphic F-contraction defined on partial metric space endowed with a directed graph. On the other hand, one more application to the existence and uniqueness of a solution for the first-order periodic boundary value problem is also provided. Our findings encompass various generalizations of the Banach contraction principle on metric space, partial metric space, and partial b-metric space. Moreover, some examples are presented to illustrate the usability of the new theory.
Fixed Points, Inner Product Spaces, and Functional Equations
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Choonkil Park
2010-01-01
Full Text Available Rassias introduced the following equality ∑i,j=1n∥xi-xj∥2=2n∑i=1n∥xi∥2, ∑i=1nxi=0, for a fixed integer n≥3. Let V,W be real vector spaces. It is shown that, if a mapping f:V→W satisfies the following functional equation ∑i,j=1nf(xi-xj=2n∑i=1nf(xi for all x1,…,xn∈V with ∑i=1nxi=0, which is defined by the above equality, then the mapping f:V→W is realized as the sum of an additive mapping and a quadratic mapping. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the above functional equation in real Banach spaces.
Convex analysis and monotone operator theory in Hilbert spaces
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...
On conditions for invertibility of difference and differential operators in weight spaces
Energy Technology Data Exchange (ETDEWEB)
Bichegkuev, Mairbek S [North-Ossetia State University, Vladikavkaz (Russian Federation)
2011-08-31
We obtain necessary and sufficient conditions for the invertibility of the difference operator D{sub E}:D(D{sub E}) subset of l{sup p}{sub {alpha}}{yields}l{sup p}{sub {alpha}}, (D{sub E} x)(n)=x(n+1)-Bx(n), n element of Z{sub +}, whose domain D(D{sub E}) is given by the condition x(0) element of E, where l{sup p}{sub {alpha}}=l{sup p}{sub {alpha}}(Z{sub +},X), p element of [1,{infinity}], is the Banach space of sequences (of vectors in a Banach space X) summable with weight {alpha}:Z{sub +}{yields}(0,{infinity}) for p element of [1,{infinity}) and bounded with respect to {alpha} for p={infinity}, B:X{yields}X is a bounded linear operator, and E is a closed B-invariant subspace of X. We give applications to the invertibility of differential operators with an unbounded operator coefficient (the generator of a strongly continuous operator semigroup) in weight spaces of functions.
Seminar on Functional Analysis at the University of Texas
Rosenthal, Haskell
1991-01-01
The papers in this volume yield a variety of powerful tools for penetrating the structure of Banach spaces, including the following topics: the structure of Baire-class one functions with Banach space applications, operator extension problems, the structure of Banach lattices tensor products of operators and Banach spaces, Banach spaces of certain classes of Fourier series, uniformly stable Banach spaces, the hyperplane conjecture for convex bodies, and applications of probability theory to local Banach space structure. With contributions by: R. Haydon, E. Odell, H. Rosenthal: On certain classes of Baire-1 functions with applications to Banach space theory.- K. Ball: Normed spaces with a weak-Gordon-Lewis property.- S.J. Szarek: On the geometry of the Banach-Mazur compactum.- P. Wojtaszczyk: Some remarks about the space of measures with uniformly bounded partial sums and Banach-Mazur distances between some spaces of polynomials.- N. Ghoussoub, W.B. Johnson: Operators which factor through Banach lattices not c...
Mutational analysis a joint framework for Cauchy problems in and beyond vector spaces
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.
Winter School on Operator Spaces, Noncommutative Probability and Quantum Groups
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...
Zegeye, Habtu; Shahzad, Naseer
2014-01-01
We introduce an iterative process for finding an element of a common fixed point of a finite family of Bregman weak relatively nonexpansive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.
On almost B-summable double sequence spaces.
Tuğ, Orhan
2018-01-01
The concept of a four-dimensional generalized difference matrix and its domain on some double sequence spaces was recently introduced and studied by Tuğ and Başar (AIP Conference Proceedings, vol. 1759, 2016) and Tuğ (J. Inequal. Appl. 2017(1):149, 2017). In this present paper, as a natural continuation of (J. Inequal. Appl. 2017(1):149, 2017), we introduce new almost null and almost convergent double sequence spaces [Formula: see text] and [Formula: see text] as the four-dimensional generalized difference matrix [Formula: see text] domain in the spaces [Formula: see text] and [Formula: see text], respectively. Firstly, we prove that the spaces [Formula: see text] and [Formula: see text] of double sequences are Banach spaces under some certain conditions. Then we give an inclusion relation of these new almost convergent double sequence spaces. Moreover, we identify the α -dual, [Formula: see text]-dual and γ -dual of the space [Formula: see text]. Finally, we characterize some new matrix classes [Formula: see text], [Formula: see text], and we complete this work with some significant results.
On asphericity of convex bodies in linear normed spaces.
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.
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
Maximal regularity in lp spaces for discrete time fractional shifted equations
Lizama, Carlos; Murillo-Arcila, Marina
2017-09-01
In this paper, we are presenting a new method based on operator-valued Fourier multipliers to characterize the existence and uniqueness of ℓp-solutions for discrete time fractional models in the form where A is a closed linear operator defined on a Banach space X and Δα denotes the Grünwald-Letnikov fractional derivative of order α > 0. If X is a UMD space, we provide this characterization only in terms of the R-boundedness of the operator-valued symbol associated to the abstract model. To illustrate our results, we derive new qualitative properties of nonlinear difference equations with shiftings, including fractional versions of the logistic and Nagumo equations.
Spectral analysis of difference and differential operators in weighted spaces
Energy Technology Data Exchange (ETDEWEB)
Bichegkuev, M S [North-Ossetia State University, Vladikavkaz (Russian Federation)
2013-11-30
This paper is concerned with describing the spectrum of the difference operator K:l{sub α}{sup p}(Z,X)→l{sub α}{sup p}(Z......athscrKx)(n)=Bx(n−1), n∈Z, x∈l{sub α}{sup 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{sub α}{sup 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.
Bause, Markus; Radu, Florin A; Köcher, Uwe
2017-01-01
Variational time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods in space for simulating transport processes have been demonstrated in a wide class of works. We consider a family of continuous Galerkin-Petrov time discretization schemes that is combined with a mixed finite element approximation of the spatial variables. The existence and uniqueness of the semidiscrete approximation and of the fully discrete solution are established. For this, the Banach-Nečas-Babuška theorem is applied in a non-standard way. Error estimates with explicit rates of convergence are proved for the scalar and vector-valued variable. An optimal order estimate in space and time is proved by duality techniques for the scalar variable. The convergence rates are analyzed and illustrated by numerical experiments, also on stochastically perturbed meshes.
A distinguished real Banach algebra
Indian Academy of Sciences (India)
Département de Mathématiques, LMAM, UMR 7122, Université Paul Verlaine,. Ile du Saulcy, F-57045 Metz, France. E-mail: mortini@poncelet.univ-metz.fr. MS received 7 December 2008; revised 20 April 2009. Abstract. We present a new and elementary approach to characterize the maximal ideals and their associated ...
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.
Adams, Robert A
2003-01-01
Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences.This second edition of Adam''s ''classic'' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike.* Self-contained and accessible for readers in other disciplines.* Written at elementary level making it accessible to graduate students.
Adelstein, Pamela
2018-01-01
A space can be sacred, providing those who inhabit a particular space with sense of transcendence-being connected to something greater than oneself. The sacredness may be inherent in the space, as for a religious institution or a serene place outdoors. Alternatively, a space may be made sacred by the people within it and events that occur there. As medical providers, we have the opportunity to create sacred space in our examination rooms and with our patient interactions. This sacred space can be healing to our patients and can bring us providers opportunities for increased connection, joy, and gratitude in our daily work.
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.
Generalized Hyers-Ulam Stability of Quadratic Functional Inequality
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Hark-Mahn Kim
2013-01-01
Full Text Available We establish the general solution of the functional inequality and then investigate the generalized Hyers-Ulam stability of this inequality in Banach spaces and in non-Archimedean Banach spaces.
As well as authorizing NASA's funding for FY 1998 and 1999, the Civilian Space Authorization Act (H.R. 1275) would affect U.S.-Russia interactions in space. Regarding the International Space Station, the bill: prohibits transferring funds to Russia to pay for work on elements that are Russia's responsibility;
Worthington, Scott; Worthington, Scott
2015-01-01
My dissertation consists of two parts. The larger portion is an hour-long piece for double bass, electronics, and projected text called Space Administration. The second portion, this essay, discusses my musical background leading up to Space Administration, details of the composition itself, and what new directions I see in my work that in part stem from creating the piece Space Administration
Model Classes, Approximation, and Metrics for Dynamic Processing of Urban Terrain Data
2013-01-01
Lawrence Livermore National Laboratory “Compressive Signal Processing,” Mohammed Dahleh Distinguished Lecture, UCSB "Greedy Algorithms in Banach Spaces ...in Banach Spaces ", Davinci Lecture Series, Milan, Italy, July 2012 "Greedy Algorithms in Banach Spaces ", Departmental Series, Aachen, Germany, July...sensing and Related Applica- tions, 12/2010, Seoul, Korea. R. DeVore, Greedy Algorithms in Banach Spaces , Davinci Lecture Series, Milan, Italy, July
DEFF Research Database (Denmark)
2005-01-01
of digital technology with space poses new challenges that call for new approaches. Creative alternatives to traditional systems methodologies are called for when designers use digital media to create new possibilities for action in space. Design Spaces explores how design and media art can provide creative......Digital technologies and media are becoming increasingly embodied and entangled in the spaces and places at work and at home. However, our material environment is more than a geometric abstractions of space: it contains familiar places, social arenas for human action. For designers, the integration...... alternatives for integrating digital technology with space. Connecting practical design work with conceptual development and theorizing, art with technology, and usesr-centered methods with social sciences, Design Spaces provides a useful research paradigm for designing ubiquitous computing. This book...
DEFF Research Database (Denmark)
2005-01-01
Digital technologies and media are becoming increasingly embodied and entangled in the spaces and places at work and at home. However, our material environment is more than a geometric abstractions of space: it contains familiar places, social arenas for human action. For designers, the integration...... of digital technology with space poses new challenges that call for new approaches. Creative alternatives to traditional systems methodologies are called for when designers use digital media to create new possibilities for action in space. Design Spaces explores how design and media art can provide creative...... alternatives for integrating digital technology with space. Connecting practical design work with conceptual development and theorizing, art with technology, and usesr-centered methods with social sciences, Design Spaces provides a useful research paradigm for designing ubiquitous computing. This book...
Martin, Gary L.
2011-01-01
A robust and competitive commercial space sector is vital to continued progress in space. The United States is committed to encouraging and facilitating the growth of a U.S. commercial space sector that supports U.S. needs, is globally competitive, and advances U.S. leadership in the generation of new markets and innovation-driven entrepreneurship. Energize competitive domestic industries to participate in global markets and advance the development of: satellite manufacturing; satellite-based services; space launch; terrestrial applications; and increased entrepreneurship. Purchase and use commercial space capabilities and services to the maximum practical extent Actively explore the use of inventive, nontraditional arrangements for acquiring commercial space goods and services to meet United States Government requirements, including measures such as public-private partnerships, . Refrain from conducting United States Government space activities that preclude, discourage, or compete with U.S. commercial space activities. Pursue potential opportunities for transferring routine, operational space functions to the commercial space sector where beneficial and cost-effective.
Existence of solutions of nonlinear integrodifferential equations of ...
Indian Academy of Sciences (India)
of solutions of semilinear evolution equations of Sobolev type in Banach spaces. This type of equations ... in a Banach space X and ranges contained in a Banach space Y and the nonlinear. Proc. Indian Acad. Sci. ... From the above fact and the closed graph theorem imply the boundedness of the linear operator AB└1 : Y 3 ...
Pelczynski's property (V) and weak* basic sequences | Cilia ...
African Journals Online (AJOL)
In this note we study the property (V) of Pelczynski, in a Banach space X, in relation with the presence, in the dual Banach space X*, of suitable weak* basic sequences. We answer negatively to a question posed by John and we prove that, if X is a Banach space with the Property (V) of Pelczynski and the Gelfand Phillips ...
Indian Academy of Sciences (India)
This talk deals with the geometry of Banach spaces. A non-reflexive Banach space embeds canonically in its second dual and the process continues, giving raise to a strictly increasing chain of Banach spaces. A well known example of a geometric phenomenon that is preserved in this chain, is that of being (isometric) a ...
Fixed Point Theory for Lipschitzian-type Mappings with Applications
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.
2014-06-30
set of methods, many of which have their origin in probability in Banach spaces , that arise across a broad range of contemporary problems in di↵erent...salesman problem, . . . • Probability in Banach spaces : probabilistic limit theorems for Banach - valued random variables, empirical processes, local...theory of Banach spaces , geometric functional analysis, convex geometry. • Mixing times and other phenomena in high-dimensional Markov chains. At
Berberian, S K
2002-01-01
A detailed exposition of G.W. Mackey's theory of Borel spaces (standard, substandard, analytic), based on results in Chapter 9 of Bourbaki's General Topology. Appended are five informal lectures on the subject (given at the CIMPA/ICPAM Summer School, Nice, 1986), sketching the connection between Borel spaces and representations of operator algebras.
Parin, V. V.; Gorbov, F. D.; Kosmolinskiy, F. P.
1974-01-01
Psychological selection of astronauts considers mental responses and adaptation to the following space flight stress factors: (1) confinement in a small space; (2) changes in three dimensional orientation; (3) effects of altered gravity and weightlessness; (4) decrease in afferent nerve pulses; (5) a sensation of novelty and danger; and (6) a sense of separation from earth.
DEFF Research Database (Denmark)
Svaneklink, Annette
2009-01-01
that can be related to traditional architectural concepts in terms of dealing with space, body, time and movement. The paper considers this performativity and dual spatiality as being a processual architecture, constantly reconfiguring new hybrids between space, image and user. This dual spatiality raises...
Horneck, Gerda; Klaus, David M.; Mancinelli, Rocco L.
2010-01-01
Summary: The responses of microorganisms (viruses, bacterial cells, bacterial and fungal spores, and lichens) to selected factors of space (microgravity, galactic cosmic radiation, solar UV radiation, and space vacuum) were determined in space and laboratory simulation experiments. In general, microorganisms tend to thrive in the space flight environment in terms of enhanced growth parameters and a demonstrated ability to proliferate in the presence of normally inhibitory levels of antibiotics. The mechanisms responsible for the observed biological responses, however, are not yet fully understood. A hypothesized interaction of microgravity with radiation-induced DNA repair processes was experimentally refuted. The survival of microorganisms in outer space was investigated to tackle questions on the upper boundary of the biosphere and on the likelihood of interplanetary transport of microorganisms. It was found that extraterrestrial solar UV radiation was the most deleterious factor of space. Among all organisms tested, only lichens (Rhizocarpon geographicum and Xanthoria elegans) maintained full viability after 2 weeks in outer space, whereas all other test systems were inactivated by orders of magnitude. Using optical filters and spores of Bacillus subtilis as a biological UV dosimeter, it was found that the current ozone layer reduces the biological effectiveness of solar UV by 3 orders of magnitude. If shielded against solar UV, spores of B. subtilis were capable of surviving in space for up to 6 years, especially if embedded in clay or meteorite powder (artificial meteorites). The data support the likelihood of interplanetary transfer of microorganisms within meteorites, the so-called lithopanspermia hypothesis. PMID:20197502
Directory of Open Access Journals (Sweden)
Alex Ellery
2004-09-01
Full Text Available In this second of three short papers, I introduce some of the basic concepts of space robotics with an emphasis on some specific challenging areas of research that are peculiar to the application of robotics to space infrastructure development. The style of these short papers is pedagogical and the concepts in this paper are developed from fundamental manipulator robotics. This second paper considers the application of space manipulators to on-orbit servicing (OOS, an application which has considerable commercial application. I provide some background to the notion of robotic on-orbit servicing and explore how manipulator control algorithms may be modified to accommodate space manipulators which operate in the micro-gravity of space.
Kellett, B. J.; Griffin, D. K.; Bingham, R.; Campbell, R. N.; Forbes, A.; Michaelis, M. M.
2008-05-01
Hybrid space propulsion has been a feature of most space missions. Only the very early rocket propulsion experiments like the V2, employed a single form of propulsion. By the late fifties multi-staging was routine and the Space Shuttle employs three different kinds of fuel and rocket engines. During the development of chemical rockets, other forms of propulsion were being slowly tested, both theoretically and, relatively slowly, in practice. Rail and gas guns, ion engines, "slingshot" gravity assist, nuclear and solar power, tethers, solar sails have all seen some real applications. Yet the earliest type of non-chemical space propulsion to be thought of has never been attempted in space: laser and photon propulsion. The ideas of Eugen Saenger, Georgii Marx, Arthur Kantrowitz, Leik Myrabo, Claude Phipps and Robert Forward remain Earth-bound. In this paper we summarize the various forms of nonchemical propulsion and their results. We point out that missions beyond Saturn would benefit from a change of attitude to laser-propulsion as well as consideration of hybrid "polypropulsion" - which is to say using all the rocket "tools" available rather than possibly not the most appropriate. We conclude with three practical examples, two for the next decades and one for the next century; disposal of nuclear waste in space; a grand tour of the Jovian and Saturnian moons - with Huygens or Lunoxod type, landers; and eventually mankind's greatest space dream: robotic exploration of neighbouring planetary systems.
Doignon, Jean-Paul
1999-01-01
Knowledge spaces offer a rigorous mathematical foundation for various practical systems of knowledge assessment. An example is offered by the ALEKS system (Assessment and LEarning in Knowledge Spaces), a software for the assessment of mathematical knowledge. From a mathematical standpoint, knowledge spaces generalize partially ordered sets. They are investigated both from a combinatorial and a stochastic viewpoint. The results are applied to real and simulated data. The book gives a systematic presentation of research and extends the results to new situations. It is of interest to mathematically oriented readers in education, computer science and combinatorics at research and graduate levels. The text contains numerous examples and exercises and an extensive bibliography.
DEFF Research Database (Denmark)
Birke, Alexander; Schoenau-Fog, Henrik; Reng, Lars
2012-01-01
This paper presents Space Bugz! - a novel crowd game for large venues or cinemas that utilises the audience's smartphones as controllers for the game. This paper explains what crowd gaming is and describes how the approach used in Space Bugz! enables more advanced gameplay concepts and individual...... player control than current technologies allow. The gameplay of Space Bugz! is then explained along with the technical architecture of the game. After this, the iterative design process used to create the game is described together with future perspectives. The article concludes with links to a video...
Zaanen, A C
1983-01-01
While Volume I (by W.A.J. Luxemburg and A.C. Zaanen, NHML Volume 1, 1971) is devoted to the algebraic aspects of the theory, this volume emphasizes the analytical theory of Riesz spaces and operators between these spaces. Though the numbering of chapters continues on from the first volume, this does not imply that everything covered in Volume I is required for this volume, however the two volumes are to some extent complementary.
International Nuclear Information System (INIS)
Doke, Tadayoshi
1988-01-01
Japan will take part in the LML-1 (International Microgravity Laboratory 1) program that is scheduled to be carried out with space shuttles to be launched in 1991. The program will be followed by the LS-J (Space Laboratory-Japan) and IML-2 programs. A reliable dosimetry system is currently required to be established to evaluate the radiations in space. The present article reviews major features of different types of space radiations and requirements of dosimeters for these radiations. The radiations in the space environment consist of: 1) electrons and protons that have been trapped by the terrestrial magnetism, 2) corpuscular, gamma-and X-rays released from the sun, and 3) galactic cosmic rays (corpuscular, gamma-and X-rays). The effects of the trapped radiations will be low if a spacecraft can get through the zone of such radiations in a short period of time. The effects of galactic cosmic rays are much smaller than those of the trapped radiations. A solar flare can give significant contributions to the total radiations received by a spacecraft. An extremely large flare can release a fatal amount of radiations to the crew of a spacecraft. Prediction of such a large flare is of great important for a long trip through the space. Significant improvements should be made on existing dosimeters. (Nogami, K.)
Robust Computation of Linear Models, or How to Find a Needle in a Haystack
2012-02-17
theory, random matrices and Banach spaces . In Handbook of the geometry of Banach spaces , Vol. I, pages 317–366. North-Holland, Amsterdam, 2001. [DS03...K. R. Davidson and S. J. Szarek. Addenda and corrigenda to: “Local operator theory, random matrices and Banach spaces ” [in Handbook of the geometry...of Banach spaces , Vol. I, 317–366, North-Holland, Amsterdam, 2001; MR1863696 (2004f:47002a)]. In Handbook of the geometry of Banach spaces , Vol. 2
Directory of Open Access Journals (Sweden)
Elena Grigoryeva
2013-01-01
Full Text Available The topic of this issue is PUBLIC SPACES. It is familiar and clear to every citizen. The streets and courtyards as childhood experiences remain with us forever. And these are the places where we come with our parents at weekends, where we meet friends, where we have dates and where we already come for a walk with our children.The history of public spaces is long and captivating. It was the main city squares where the most important events took place in history. The Agoras of Ancient Greece and the Roman Forums, the squares of Vatican, Paris and London, Moscow and Saint Petersburg… Greve, Trafalgar, Senate, Palace, Red, Bolotnaya – behind every name there is life of capitals, countries and nations.Public spaces, their shapes, image and development greatly influence the perception of the city as a whole. Both visitors and inhabitants can see in public spaces not only the visage but the heart, the soul and the mind of the city.Unfortunately, sometimes we have to prove the value of public spaces and defend them from those who consider them nothing but a blank space, nobody’s land destined for barbarous development.What should happen to make citizens perceive public spaces as their own and to make authorities consider development and maintenance of squares and parks their priority task against the background of increasing competition between cities and the fight for human capital? Lately they more often say about “a high-quality human capital”. And now, when they say “the city should be liveable” they add “for all groups of citizens, including the creative class”.
Underground spaces/cybernetic spaces
Directory of Open Access Journals (Sweden)
Tomaž Novljan
2000-01-01
Full Text Available A modern city space is a space where in the vertical and horizontal direction dynamic, non-linear processes exist, similar as in nature. Alongside the “common” city surface, cities have underground spaces as well that are increasingly affecting the functioning of the former. It is the space of material and cybernetic communication/transport. The psychophysical specifics of using underground places have an important role in their conceptualisation. The most evident facts being their limited volume and often limited connections to the surface and increased level of potential dangers of all kinds. An efficient mode for alleviating the effects of these specific features are artistic interventions, such as: shape, colour, lighting, all applications of the basic principles of fractal theory.
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.
DEFF Research Database (Denmark)
Larsen, Henrik Gutzon
Using the development of intergovernmental environmental cooperation in the Baltic Sea area as a concrete example, the aim of this study is to explore how the 'environment' in situations of environmental interdependence is identified and institutionalised as political-geographical objects....... 'Environmental interdependence' is to this end conceptualised as a tension between 'political spaces' of discrete state territories and 'environmental spaces' of spatially nested ecosystems. This tension between geographies of political separateness and environmental wholeness is the implicit or explicit basis...... for a large and varied literature. But in both its critical and problemsolving manifestations, this literature tends to naturalise the spatiality of environmental concerns: environmental spaces are generally taken for granted. On the suggestion that there is a subtle politics to the specification...
Decentralized Riemannian Particle Filtering with Applications to Multi-Agent Localization
2012-06-14
166 A.5 Hilbert and Banach Spaces . . . . . . . . . . . . . . . . . . 168 Bibliography...metric spaces ! A.5 Hilbert and Banach Spaces Definition A.5.1. A Hilbert spaceH is a vector space endowed with an inner product and associated norm and...that every Cauchy sequence takes a limit in Rn. This makes Rn a Hilbert space . Definition A.5.2. A Banach space B is a normed space with associated
Rega, Joseph Mark
2003-01-01
Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Comunicação e Expressão. Programa de Pós-Graduação em Inglês e Literatura Correspondente. The recent surge in cyberspace science fiction follows previous trends within the genre, i.e. those connected with future city-space and outer space, and is an inevitable result of economic forces. There has always been a close relationship between capitalism and spatial expansion, compelled by technological innovations that ha...
Petrov, Aleksej Z
1969-01-01
Einstein Spaces presents the mathematical basis of the theory of gravitation and discusses the various spaces that form the basis of the theory of relativity. This book examines the contemporary development of the theory of relativity, leading to the study of such problems as gravitational radiation, the interaction of fields, and the behavior of elementary particles in a gravitational field. Organized into nine chapters, this book starts with an overview of the principles of the special theory of relativity, with emphasis on the mathematical aspects. This text then discusses the need for a ge
Zubrin, Robert
The authors is giving a classification of civilisations depending on the degree of colonisation of the Earth, Solar System and Our Galaxy. The problems of: History of geographic discoveries (The great geographical discoveries during the Middle Age, the concurence of Chinnese and Europeans in this Area); The Astrophysics, such as: Asteroids, Water and Atmosphere on outer planets, Planet Mars Planet, Agriculture on outer planets, Minerals on outer planets; Cosmic flights: Fuels, Robotics, Moon (as an intermediary basis for interplanetary flights), Mars colonisation; Interstellar flights, Space research costs, strategy and tactics of the space colonisation; Policy: War and Peace, International Collaboration are discussed.
DEFF Research Database (Denmark)
Raahauge, Kirsten Marie
2008-01-01
This article deals with representations of one specific city, Århus, Denmark, especially its central district. The analysis is based on anthropological fieldwork conducted in Skåde Bakker and Fedet, two well-off neighborhoods. The overall purpose of the project is to study perceptions of space...... and the interaction of cultural, social, and spatial organizations, as seen from the point of view of people living in Skåde Bakker and Fedet. The focus is on the city dwellers’ representations of the central district of Århus with specific reference to the concept of transit space. When applied to various Århusian...
2013-06-24
with the Hahn- Banach theorem yields a "weak" representation of the norm on X, Theorem 1.23 If X is a Banach space , then ||x||x = sup Ä = sup \\y...1.3.2 The adjoint operator To motivate the definition of the adjoint operator, let X and Y be two Banach spaces . L : X —► Y be a continuous linear...1.30 If X is a normed vector space over R, then X* is a Banach space , i.e. Cauchy sequences in X converge to a limit in X, whether or not X is a Banach