Casazza, Peter G.; Lammers, Mark C.
1999-01-01
We show that the classification problem for genus $n$ Banach spaces can be reduced to the unconditionally primary case and that the critical case there is $n=2$. It is further shown that a genus $n$ Banach space is unconditionally primary if and only if it contains a complemented subspace of genus $(n-1)$. We begin the process of classifying the genus 2 spaces by showing they have a strong decomposition property.
Multipliers of Banach valued weighted function spaces
Directory of Open Access Journals (Sweden)
Serap Öztop
2000-10-01
Full Text Available We generalize Banach valued spaces to Banach valued weighted function spaces and study the multipliers space of these spaces. We also show the relationship between multipliers and tensor product of Banach valued weighted function spaces.
Separably injective Banach spaces
Avilés, Antonio; Castillo, Jesús M F; González, Manuel; Moreno, Yolanda
2016-01-01
This monograph contains a detailed exposition of the up-to-date theory of separably injective spaces: new and old results are put into perspective with concrete examples (such as l∞/c0 and C(K) spaces, where K is a finite height compact space or an F-space, ultrapowers of L∞ spaces and spaces of universal disposition). It is no exaggeration to say that the theory of separably injective Banach spaces is strikingly different from that of injective spaces. For instance, separably injective Banach spaces are not necessarily isometric to, or complemented subspaces of, spaces of continuous functions on a compact space. Moreover, in contrast to the scarcity of examples and general results concerning injective spaces, we know of many different types of separably injective spaces and there is a rich theory around them. The monograph is completed with a preparatory chapter on injective spaces, a chapter on higher cardinal versions of separable injectivity and a lively discussion of open problems and further lines o...
$\\alpha$-minimal Banach spaces
Rosendal, Christian
2011-01-01
A Banach space with a Schauder basis is said to be $\\alpha$-minimal for some countable ordinal $\\alpha$ if, for any two block subspaces, the Bourgain embeddability index of one into the other is at least $\\alpha$. We prove a dichotomy that characterises when a Banach space has an $\\alpha$-minimal subspace, which contributes to the ongoing project, initiated by W. T. Gowers, of classifying separable Banach spaces by identifying characteristic subspaces.
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...
A pythagorean approach in Banach spaces
Gao Ji
2006-01-01
Let be a Banach space and let be the unit sphere of . Parameters , , , and , where and are introduced and studied. The values of these parameters in the spaces and function spaces are estimated. Among the other results, we proved that a Banach space with , or is uniform nonsquare; and a Banach space with , or has uniform normal structure.
Fusion Frames and -Frames in Banach Spaces
Indian Academy of Sciences (India)
Amir Khosravi; Behrooz Khosravi
2011-05-01
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 show that -frames, fusion frames and Banach -frames are stable under small perturbations and invertible operators.
Tokarev, Eugene
2002-01-01
In the article is introduced a new class of Banach spaces that are called sub B-convex. Namely, a Banach space X is said to be B -convex if it may be represented as a direct sum l_1+ W, where W is B-convex. It will be shown that any separable sub B-convex Banach space X may be almost isometrically embedded in a separable Banach space G(X) of the same cotype as X, which has a series of properties. Namely, G(X) is an approximate envelope, i.e. any separable Banach space which is finitely repres...
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....
Isometries on Banach spaces function spaces
Fleming, Richard J
2002-01-01
Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise, Banach showed that every linear isometry on the space of continuous functions on a compact metric space must transform a continuous function x into a continuous function y satisfying y(t) = h(t)x(p(t)), where p is a homeomorphism and |h| is identically one.Isometries on Banach Spaces: Function Spaces is the first of two planned volumes that survey investigations of Banach-space isometries. This volume emphasizes the characterization of isometries and focuses on establishing the type of explicit, canonical form given above in a variety of settings. After an introductory discussion of isometries in general, four chapters are devoted to describing the isometries on classical function spaces. The final chapter explores isometries on Banach algebras.This treatment p...
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
Coefficient Quantization for Frames in Banach Spaces
Casazza, P. G.; Dilworth, S. J.; Odell, E.; Schlumprecht, Th.; Zsak, Andras
2007-01-01
Let $(e_i)$ be a fundamental system of a Banach space. We consider the problem of approximating linear combinations of elements of this system by linear combinations using quantized coefficients. We will concentrate on systems which are possibly redundant. Our model for this situation will be frames in Banach spaces.
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
Simultaneous approximation in scales of Banach spaces
International Nuclear Information System (INIS)
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
Bloch spaces on bounded symmetric domains in complex Banach spaces
Institute of Scientific and Technical Information of China (English)
DENG; Fangwen
2006-01-01
We give a definition of Bloch space on bounded symmetric domains in arbitrary complex Banach space and prove such function space is a Banach space. The properties such as boundedness, compactness and closed range of composition operators on such Bloch space are studied.
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.
The cofinal property of the Reflexive Indecomposable Banach spaces
Argyros, Spiros A.; Raikoftsalis, Theocharis
2010-01-01
It is shown that every separable reflexive Banach space is a quotient of a reflexive Hereditarily Indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive Indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably $\\ell_p$ saturated space with $1
A Gaussian Average Property for Banach Spaces
Casazza, Peter G.; Nielsen, Niels Jorgen
1996-01-01
In this paper we investigate a Gaussian average property of Banach spaces. This property is weaker than the Gordon Lewis property but closely related to this and other unconditional structures. It is also shown that this property implies that certain Hilbert space valued operators defined on subspaces of the given space can be extended.
On Banach spaces without the approximation property
Reinov, Oleg I.
2002-01-01
A. Szankowski's example is used to construct a Banach space similar to that of "An example of an asymptotically Hilbertian space which fails the approximation property", P.G. Casazza, C.L. Garc\\'{\\i}a, W.B. Johnson [math.FA/0006134 ()].
Boundary Controllability of Integrodifferential Systems in Banach Spaces
Indian Academy of Sciences (India)
K Balachandran; E R Anandhi
2001-02-01
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.
The Topological Degree in Ordered Banach Spaces
Institute of Scientific and Technical Information of China (English)
Adrian DUMA; Ileana DUMA
2008-01-01
This paper is devoted to the applications of classical topological degrees to nonlinear problems involving various classes of operators acting between ordered Banach spaces. In this frame-work, the Leray-Schauder, Browder-Petryshyn, and Amann-Weiss degree theories are considered, and several existence results are obtained. The non-Archimedean case is also discussed.
Noncompact Perturbation of Sweeping Process with Delay in Banach Spaces
A. G. Ibrahim; Aladsani, F.
2013-01-01
We have proven an existence theorem concerning the existence of solutions for a functional evolution inclusion governed by sweeping process with closed convex sets depending on time and state and with a noncompact nonconvex perturbation in Banach spaces. This work extends some recent existence theorems concerning sweeping processes from Hilbert spaces setting to Banach spaces setting. Moreover, it improves some recent existence results for sweeping processes in Banach spaces.
Reflexive Operator Algebras on Banach Spaces
Merlevède, Florence; Peligrad, Costel; Peligrad, Magda
2012-01-01
In this paper we study the reflexivity of a unital strongly closed algebra of operators with complemented invariant subspace lattice on a Banach space. We prove that if such an algebra contains a complete Boolean algebra of projections of finite uniform multiplicity and with the direct sum property, then it is reflexive, i.e. it contains every operator that leaves invariant every closed subspace in the invariant subspace lattice of the algebra. In particular, such algebras coincide with their...
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
Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions
Betancor, Jorge J; Rodríguez-Mesa, Lourdes
2011-01-01
In this paper we consider the space $BMO_o(\\mathbb{R},X)$ of bounded mean oscillations and odd functions on $\\mathbb{R}$ taking values in a UMD Banach space $X$. The functions in $BMO_o(\\mathbb{R},X)$ are characterized by Carleson type conditions involving Bessel convolutions and $\\gamma$-radonifying norms. Also we prove that the UMD Banach spaces are the unique Banach spaces for which certain $\\gamma$-radonifying Carleson inequalities for Bessel-Poisson integrals of $BMO_o(\\mathbb{R},X)$ functions hold.
Malliavin calculus and decoupling inequalities in Banach spaces
Maas, Jan
2008-01-01
We develop a theory of Malliavin calculus for Banach space valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Ito isometry to Banach spaces. In the white noise case we obtain two sided L^p-estimates for multiple stochastic integrals in arbitrary Banach spaces. It is shown that the Malliavin derivative is bounded on vector-valued Wiener-Ito chaoses. Our main tools are decoupling inequalities for vector-valued random variables. In the ...
Extremely strict ideals in Banach spaces
Indian Academy of Sciences (India)
T S S R K RAO
2016-08-01
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 functions on $K$. For injective tensor product spaces, we prove a cancelation theorem for extremely strict ideals. We also exhibit non-reflexive Banach spaces which are not strict ideals in their fourth dual.
Introduction to Banach spaces and algebras
Allan, Graham
2010-01-01
Banach spaces and algebras are a key topic of pure mathematics. Graham Allan's careful and detailed introductory account will prove essential reading for anyone wishing to specialise in functional analysis and is aimed at final year undergraduates or masters level students. Based on the author's lectures to fourth year students at Cambridge University, the book assumes knowledge typical of first degrees in mathematics, including metric spaces, analytic topology, and complexanalysis. However, readers are not expected to be familiar with the Lebesgue theory of measure and integration.The text be
Unbounded operators on Banach spaces over the quaternion field
Ludkovsky, S. V.
2004-01-01
Resolvents of quasi-linear operators and operator algebras in Banach spaces over the quaternion field are investigated. Spectral theory of unbounded nonlinear operators in quaternion Banach spaces is studied. Strongly continuous semigroups of quaternion quasi-linear operators are investigated and the polar decomposition theorem for them is proved.
The heart of the Banach spaces
Wegner, Sven-Ake
2016-01-01
Let an exact category in the sense of Quillen be given. Assume that in this category every morphism has a kernel and that every kernel is an inflation. In their famous 1982 paper, Beilinson, Bernstein and Deligne consider in this situation a t-structure on the derived category and remark that its heart can be described as a category of formal quotients. They further point out, that the category of Banach spaces is an example, and that here a similar category of formal quotients was studied by...
BANACH CONTRACTION PRINCIPLE ON CONE RECTANGULAR METRIC SPACES
Directory of Open Access Journals (Sweden)
Ismat Beg
2009-08-01
Full Text Available We introduce the notion of cone rectangular metric space and prove {sc Banach} contraction mapping principle in cone rectangular metric space setting. Our result extends recent known results.
On Shrinking and Boundedly Complete Schauder Frames of Banach spaces
Liu, Rui
2009-01-01
This paper studies Schauder frames in Banach spaces, a concept which is a natural generalization of frames in Hilbert spaces and Schauder bases in Banach spaces. The associated minimal and maximal spaces are introduced, as are shrinking and boundedly complete Schauder frames. Our main results extend the classical duality theorems on bases to the situation of Schauder frames. In particular, we will generalize James' results on shrinking and boundedly complete bases to frames. Secondly we will ...
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 ...
On the uniqueness of minimal projections in Banach spaces
Ewa Szlachtowska; Dominik Mielczarek
2012-01-01
Let \\(X\\) be a uniformly convex Banach space with a continuous semi-inner product. We investigate the relation of orthogonality in \\(X\\) and generalized projections acting on \\(X\\). We prove uniqueness of orthogonal and co-orthogonal projections.
Some Questions Arising from the Homogeneous Banach Space Problem
Casazza, Peter G.
1992-01-01
We review the current state of the homogeneous Banach space problem. We then formulate several questions which arise naturally from this problem, some of which seem to be fundamental but new. We give many examples defining the bounds on the problem. We end with a simple construction showing that every infinite dimensional Banach space contains a subspace on which weak properties have become stable (under passing to further subspaces). Implications of this construction are considered.
Construction of generalized atomic decompositions in Banach spaces
Directory of Open Access Journals (Sweden)
Raj Kumar
2014-06-01
Full Text Available G-atomic decompositions for Banach spaces with respect to a model space of sequences have been introduced and studied as a generalization of atomic decompositions. Examples and counter example have been provided to show its existence. It has been proved that an associated Banach space for G-atomic decomposition always has a complemented subspace. The notion of a representation system is introduced and exhibits its relation with G-atomic decomposition. Also It has been observed that G-atomic decompositions are exactly compressions of Schauder decompositions for a larger Banach space. We give a characterization for finite G-atomic decomposition in terms of finite-dimensional expansion of identity. Keywords: complemented coefficient spaces, finite-dimensional expansion of identity, G-atomic decomposition, representation system.
Metric embeddings bilipschitz and coarse embeddings into Banach spaces
Ostrovskii, Mikhail I
2013-01-01
Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology. The book will help readers to enter and to work in this very rapidly developing area having many important connections with different parts of mathematics and computer science. The purpose of the book is to present some of the most important techniques and results, mostly on bilipschitz and coarse embeddings. The topics include embeddability of locally finite metric spaces into Banach spaces is finitely determined, constructions of embeddings, distortion in terms of Poinc
Atomic decompositions of Banach-space-valued martingales
Institute of Scientific and Technical Information of China (English)
刘培德; 侯友良
1999-01-01
Several theorems for atomic decompositions of Banach-space-valued martingales are proved. As their applications, the relationship among some martingale spaces such as H_α(X) and _ρ(?)_α in the case 0<α≤1 are studied. It is shown that there is a close connection between the results and the smoothness and convexity of the value spaces.
Banach Spaces with respect to Operator-Valued Norms
Kim, Yun-Su
2008-01-01
We introduce the notions of L(H)-valued norms and Banach spaces with respect to L(H)-valued norms. In particular, we introduce Hilbert spaces with respect to L(H)-valued inner products. In addition, we provide several fundamental examples of Hilbert spaces with respect to L(H)-valued inner products.
A GLIDING HUMP PROPERTY AND BANACH-MACKEY SPACES
Directory of Open Access Journals (Sweden)
CHARLES SWARTZ
2001-08-01
Full Text Available We consider the Banach-Mackey property for pairs of vector spaces E and E' which are in duality. Let A be an algebra of sets and assume that P is an additive map from A into the projection operators on E. We define a continuous gliding hump property for the map P and show that pairs with this gliding hump property and anoter measure theoretic property are Banach-Mackey pairs, i. e., weakly bounded subsets of E are strongly bounded. Examples of vector valued function spaces, such as the space of Pettis integrable functions, which satisfy these conditions are given
(s, μ)-similar operators in the Banach spaces
International Nuclear Information System (INIS)
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
Banach's space: Lviv and the Scottish cafe
Directory of Open Access Journals (Sweden)
D.Henderson
2004-01-01
Full Text Available In a sense Stefan Banach is the patron saint of this workshop. He was one of the most prominent former residents of Lviv. His ``hangout'', the Scottish Cafe, is shown in the street scene that is the cover of the book of abstracts.
Riesz Isomorphisms of Tensor Products of Order Unit Banach Spaces
Indian Academy of Sciences (India)
T S S R K Rao
2009-06-01
In this paper we formulate and prove an order unit Banach space version of a Banach–Stone theorem type theorem for Riesz isomorphisms of the space of vector-valued continuous functions. Similar results were obtained recently for the case of lattice-valued continuous functions in [5] and [6].
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...
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 nonlocal problems for fractional differential equations in Banach spaces
Directory of Open Access Journals (Sweden)
XiWang Dong
2011-01-01
Full Text Available In this paper, we study the existence and uniqueness of solutions to the nonlocal problems for the fractional differential equation in Banach spaces. New sufficient conditions for the existence and uniqueness of solutions are established by means of fractional calculus and fixed point method under some suitable conditions. Two examples are given to illustrate the results.
Improved bounds in the metric cotype inequality for Banach spaces
Giladi, Ohad; Naor, Assaf
2010-01-01
It is shown that if (X, ||.||_X) is a Banach space with Rademacher cotype q then for every integer n there exists an even integer m X we have \\sum_{j=1}^n \\Avg_x [ ||f(x+ (m/2) e_j)-f(x) ||_X^q ] n^{(1/2)+(1/q)}.
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
Multipliers of pg-Bessel sequences in Banach spaces
Abdollahpour, M. R.; Najati, A.; Gavruta, P.
2015-01-01
In this paper, we introduce (p,q)g-Bessel multipliers in Banach spaces and we show that under some conditions a (p,q)g-Bessel multiplier is invertible. Also, we show the continuous dependency of (p,q)g-Bessel multipliers on their parameters.
Quantitative coarse embeddings of quasi-Banach spaces into a Hilbert space
Kraus, Michal
2015-01-01
We study how well a quasi-Banach space can be coarsely embedded into a Hilbert space. Given any quasi-Banach space X which coarsely embeds into a Hilbert space, we compute its Hilbert space compression exponent. We also show that the Hilbert space compression exponent of X is equal to the supremum of the amounts of snowflakings of X which admit a bi-Lipschitz embedding into a Hilbert space.
Factorization of weakly compact operators between Banach spaces and Fréchet or (LB)-spaces
Bonet Solves, José Antonio; Wright, J. D. Maitland
2012-01-01
In this note we show that weakly compact operators from a Banach space X into a complete (LB)-space E need not factorize through a reflexive Banach space. If E is a Fréchet space, then weakly compact operators from a Banach space X into E factorize through a reflexive Banach space. The factorization of operators from a Fréchet or a complete (LB)-space into a Banach space mapping bounded sets into relatively weakly compact sets is also investigated.
Jeribi, Aref
2015-01-01
Uncover the Useful Interactions of Fixed Point Theory with Topological StructuresNonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications is the first book to tackle the topological fixed point theory for block operator matrices with nonlinear entries in Banach spaces and Banach algebras. The book provides researchers and graduate students with a unified survey of the fundamental principles of fixed point theory in Banach spaces and algebras. The authors present several exten
Consistency of Regularized Learning Schemes in Banach Spaces
Combettes, Patrick L.; Salzo, Saverio; Villa, Silvia
2014-01-01
This paper proposes a unified framework for the investigation of learning theory in Banach spaces of features via regularized empirical risk minimization. The main result establishes the consistency of such learning schemes under general conditions on the loss function, the geometry of the feature space, the regularization function, and the regularization parameters. The focus is placed on Tikhonov-like regularization with totally convex functions. This broad class of regularizers provides a ...
Integrals and Banach spaces for finite order distributions
Talvila, Erik
2011-01-01
Let $\\Bc$ denote the real-valued functions continuous on the extended real line and vanishing at $-\\infty$. Let $\\Br$ denote the functions that are left continuous, have a right limit at each point and vanish at $-\\infty$. Define $\\acn$ to be the space of tempered distributions that are the $n$th distributional derivative of a unique function in $\\Bc$. Similarly with $\\arn$ from $\\Br$. A type of integral is defined on distributions in $\\acn$ and $\\arn$. The multipliers are iterated integrals of functions of bounded variation. For each $n\\in\\N$, the spaces $\\acn$ and $\\arn$ are Banach spaces, Banach lattices and Banach algebras isometrically isomorphic to $\\Bc$ and $\\Br$, respectively. Under the ordering in this lattice, if a distribution is integrable then its absolute value is integrable. The dual space is isometrically isomorphic to the functions of bounded variation. The space $\\ac^1$ is the completion of the $L^1$ functions in the Alexiewicz norm. The space $\\ar^1$ contains all finite signed Borel measure...
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
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
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
Some Properties of the Injective Tensor Product of Banach Spaces
Institute of Scientific and Technical Information of China (English)
Xiao Ping XUE; Yong Jin LI; Qing Ying BU
2007-01-01
Let X and Y be Banach spaces such that X has an unconditional basis. Then X?Y, the injective tensor product of X and Y, has the Radon-Nikodym property (respectively, the analytic Radon-Nikodym property, the near Radon-Nikodym property, non-containment of a copy of co, weakly sequential completeness) if and only if both X and Y have the same property and each continuous linear operator from the predual of X to Y is compact.
Tools for Malliavin calculus in UMD Banach spaces
Pronk, Matthijs
2012-01-01
In this paper we study the Malliavin derivatives and Skorohod integrals for processes taking values in an infinite dimensional space. Such results are motivated by their applications to SPDEs and in particular financial mathematics. Vector-valued Malliavin theory in Banach space E is naturally restricted to spaces E which have the so-called UMD property, which arises in harmonic analysis and stochastic integration theory. We provide several new results and tools for the Malliavin derivatives and Skorohod integrals in an infinite dimensional setting. In particular, we prove weak characterizations, a chain rule for Lipschitz functions, a sufficient condition for pathwise continuity and an Ito formula for non-adapted processes.
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.
Some Banach spaces of Dirichlet series
Bailleul, Maxime; Lefèvre, Pascal
2013-01-01
The Hardy spaces of Dirichlet series denoted by ${\\cal H}^p$ ($p\\ge1$) have been studied in [12] when p = 2 and in [3] for the general case. In this paper we study some Lp-generalizations of spaces of Dirichlet series, particularly two families of Bergman spaces denoted ${\\cal A}^p$ and ${\\cal B}^p$. We recover classical properties of spaces of analytic functions: boundedness of point evaluation, embeddings between these spaces and "Littlewood-Paley" formulas when p = 2. We also show that the...
An approximation problem of the finite rank operator in Banach spaces
Institute of Scientific and Technical Information of China (English)
王玉文; 潘少荣
2003-01-01
By the method of geometry of Banach spaces, we have proven that a bounded linear operatorin Banach space is a compact linear one iff it can be uniformly approximated by a sequence of the finite rankbounded homogeneous operators, which reveals the essence of the counter example given by Enflo.
Institute of Scientific and Technical Information of China (English)
Adrian PETRU(S)EL; Jen-Chih YAO
2009-01-01
In this paper, we prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the viscosity approximation method with a generalized contraction mapping. The proximal point algorithm in a Banach space is also considered. The results extend some very recent theorems of W. Takahashi.
On sets minimizing their weighted length in uniformly convex separable Banach spaces
De Pauw, Thierry; Lemenant, Antoine; Millot, Vincent
2013-01-01
We study existence and partial regularity relative to the weighted Steiner problem in Banach spaces. We show $C^1$ regularity almost everywhere for almost minimizing sets in uniformly rotund Banach spaces whose modulus of uniform convexity verifies a Dini growth condition.
First and Second Order Convex Sweeping Processes in Reflexive Smooth Banach Spaces
International Nuclear Information System (INIS)
In this paper we establish new characterizations of the normal cone of closed convex sets in reflexive smooth Banach spaces and then we use those results to prove the existence of solutions for first order convex sweeping processes and their variants in reflexive smooth Banach spaces. The case of second order convex sweeping processes is also studied. (author)
On moduli of convexity in Banach spaces
Reif Jiří
2005-01-01
Let be a normed linear space, an element of norm one, and and the local modulus of convexity of . We denote by the greatest such that for each closed linear subspace of the quotient mapping maps the open -neighbourhood of in onto a set containing the open -neighbourhood of in . It is known that . We prove that there is no universal constant such that , however, such a constant exists within the class of Hilbert spaces . If is a Hilbert space with , then .
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.
On nonautonomous second-order differential equations on Banach space
Directory of Open Access Journals (Sweden)
Nguyen Thanh Lan
2001-04-01
Full Text Available We show the existence and uniqueness of classical solutions of the nonautonomous second-order equation: uÃ¢Â€Â³(t=A(tuÃ¢Â€Â²(t+B(tu(t+f(t, 0Ã¢Â‰Â¤tÃ¢Â‰Â¤T; u(0=x0, uÃ¢Â€Â²(0=x1 on a Banach space by means of operator matrix method and apply to Volterra integrodifferential equations.
Iterative solutions of nonlinear equations in smooth Banach spaces
International Nuclear Information System (INIS)
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
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 Math ematics Impact factor: 0.529, year: 2012 http://oam.ele- math .com/06-15/Geometry-and-Gateaux-smoothness-in-separable-Banach-spaces
Linearization of class C1 for contractions on Banach spaces
Rodrigues, Hildebrando M.; Solà-Morales, J.
In this work we prove a C1-linearization result for contraction diffeomorphisms, near a fixed point, valid in infinite-dimensional Banach spaces. As an intermediate step, we prove a specific result of existence of invariant manifolds, which can be interesting by itself and that was needed on the proof of our main theorem. Our results essentially generalize some classical results by P. Hartman in finite dimensions, and a result of Mora-Sola-Morales in the infinite-dimensional case. It is shown that the result can be applied to some abstract systems of semilinear damped wave equations.
Near Convexity, Near Smoothness and Approximative Compactness of Half Spaces in Banach Spaces
Institute of Scientific and Technical Information of China (English)
Zi Hou ZHANG; Yu ZHOU; Chun Yan LIU
2016-01-01
The authors discuss the dual relation of nearly very convexity and property WS.By two kinds of near convexities and two kinds of near smoothness,the authors prove a series of characterizations such that every half-space in Banach space X and every weak* half-space in the dual space X* are approximatively weakly compact and approximatively compact.They show a sufficient condition such that a Banach space X is a Asplund space.Using upper semi-continuity of duality mapping,the authors also give two characterizations of property WS and property S.
On moduli of convexity in Banach spaces
Directory of Open Access Journals (Sweden)
Reif Jiří
2005-01-01
Full Text Available Let be a normed linear space, an element of norm one, and and the local modulus of convexity of . We denote by the greatest such that for each closed linear subspace of the quotient mapping maps the open -neighbourhood of in onto a set containing the open -neighbourhood of in . It is known that . We prove that there is no universal constant such that , however, such a constant exists within the class of Hilbert spaces . If is a Hilbert space with , then .
FRAME MULTIRESOLUTION ANALYSIS AND INFINITE TREES IN BANACH SPACES ON LOCALLY COMPACT ABELIAN GROUPS
Institute of Scientific and Technical Information of China (English)
S. S. Panday
2004-01-01
We extend the concept of frame multiresolution analysis to a locally compact abelian group and use it to define certain weighted Banach spaces and the spaces of their antifunctionals. We define analysis and synthesis operators on these spaces and establish the continuity of their composition. Also, we prove a general result to characterize infinite trees in the above Banach spaces of antifunctionals. This paper paves the way for the study of corresponding problems associated with some other types of Banach spaces on locally compact abelian groups including modulation spaces.
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
QUASI-LOCAL CONJUGACY THEOREMS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
ZHANG WEIRONG; MA JIPU
2005-01-01
Let f: U(xo)() E → F be a C1 map and f'(x0) be the Frechet derivative of f at x0. In local analysis of nonlinear functional analysis, implicit function theorem, inverse function theorem, local surjectivity theorem, local injectivity theorem, and the local conjugacy theorem are well known. Those theorems are established by using the properties: f'(x0) is double splitting and R(f'(x)) ∩ N(T0+) = {0} near x0. However,in infinite dimensional Banach spaces, f'(x0) is not always double splitting (i.e., the generalized inverse of f'(x0) does not always exist), but its bounded outer inverse of f'(x0) always exists.Only using the C1 map f and the outer inverse T0# of f'(x0), the authors obtain two quasi-local conjugacy theorems, which imply the local conjugacy theorem if x0 is a locally fine point of f. Hence the quasi-local conjugacy theorems generalize the local conjugacy theorem in Banach spaces.
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 $n.$
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.
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...
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}\\.
Approximative compactness and continuity of metric projector in Banach spaces and applications
Institute of Scientific and Technical Information of China (English)
HUDZIK; Henryk; KOWALEWSKI; Wojciech; WISLA; Marek
2008-01-01
First we prove that the approximative compactness of a nonempty set C in a normed linear space can be reformulated equivalently in another way.It is known that if C is a semi-Chebyshev closed and approximately compact set in a Banach space X,then the metric projectorπC from X onto C is continuous.Under the assumption that X is midpoint locally uniformly rotund,we prove that the approximative compactness of C is also necessary for the continuity of the projectorπC by the method of geometry of Banach spaces.Using this general result we find some necessary and sufficient conditions for T to have a continuous Moore-Penrose metric generalized inverse T~+,where T is a bounded linear operator from an approximative compact and a rotund Banach space X into a midpoint locally uniformly rotund Banach space Y.
On Property () in Banach Lattices, Calderón–Lozanowskiĭ and Orlicz–Lorentz Spaces
Indian Academy of Sciences (India)
Paweł Kolwicz
2001-08-01
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 study property () in Banach function lattices. Namely a criterion for property () in Banach function lattice is presented. In particular we get that in Banach function lattice property () implies uniform monotonicity. Moreover, property () in generalized Calderón–Lozanowskiĭ function spaces is studied. Finally, it is shown that in Orlicz–Lorentz function spaces property () and uniform convexity coincide.
International Nuclear Information System (INIS)
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.
Institute of Scientific and Technical Information of China (English)
张石生
2001-01-01
The purpose of this paper is to study the existence and approximation problem of solutions for a class of variational inclusions with accretive mappings in Banach spaces. The results extend and improve some recent results.
Approximating zero points of accretive operators with compact domains in general Banach spaces
Directory of Open Access Journals (Sweden)
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.
Exponential dichotomies for linear discrete-time systems in Banach spaces
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Ioan-Lucian Popa
2012-04-01
Full Text Available In this paper we investigate some dichotomy concepts for linear difference equations in Banach spaces. Characterizations of these concepts are given. Some illustrating examples clarify the relations between these concepts.
Geometrical and Topological Properties of Bumps and Starlike Bodies in Banach Spaces
Azagra Rueda, Daniel; Jiménez Sevilla, María del Mar
2002-01-01
While the topological and geometrical properties of convex bodies in Banach spaces are quite well understood (including their topological and smooth classification), much less is known about the structure of starlike bodies. Starlike bodies are important objects in nonlinear functional analysis as they appear as level sets of $n$-homogeneous polynomials on Banach spaces. Significant progress in the study of starlike bodies has been done in the last years by the efforts of Manuel Cepedello, Ro...
On quasi-convex mappings of order α in the unit ball of a complex Banach space
Institute of Scientific and Technical Information of China (English)
LIU Taishun; XU Qinghua
2006-01-01
In this paper, a class of biholomorphic mappings named quasi-convex mapping of order α in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings.Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space Ⅹ. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order α defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively.
Institute of Scientific and Technical Information of China (English)
Robert F.Allen
2014-01-01
We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient condi-tions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide ”computable” estimates on the operator norm.
Isometric uniqueness of a complementably universal Banach space for Schauder decompositions
Garbulińska, Joanna
2014-01-01
We present an isometric version of the complementably universal Banach space $\\mathbb{P}$ with a Schauder decomposition. The space $\\mathbb{P}$ is isomorphic to Pe{\\l}czy\\'nski's space with a universal basis as well as to Kadec' complementably universal space with the bounded approximation property.
Wang, Min
2016-04-01
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.
On well posedness of best simultaneous approximation problems in Banach spaces
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The well posedness of best simultaneous approximation problems is considered. We establish the generic results on the well posedness of the best simultaneous approximation problems for any closed weakly compact nonempty subset in a strictly convex Kadec Banach space. Further, we prove that the set of all points in E(G) such that the best simultaneous approximation problems are not well posed is a σ-porous set in E(G) when X is a uniformly convex Banach space. In addition, we also investigate the generic property of the ambiguous loci of the best simultaneous approximation.
Real-Analytic Negligibility of Points and Subspaces in Banach Spaces, with Applications
Azagra Rueda, Daniel; Dobrowolski, Tadeusz
2002-01-01
We prove that every infinite-dimensional Banach space X having a (not necessarily equivalent) real-analytic norm is real-analytic diffeomorphic to X \\ {0}. More generally, if X is an infinite-dimensional Banach space and F is a closed subspace of X such that there is a real-analytic seminorm on X whose set of zeros is F, and X / F is infinite-dimensional, then X and X \\ F are real-analytic diffeomorphic. As an application we show the existence of real-analytic free actions of the circle and t...
Smooth negligibility of compact sets in infinite-dimensional Banach spaces, with applications
Azagra Rueda, Daniel; Dobrowolski, Tadeusz
1998-01-01
This article deals with smooth removability of compact sets in infinite-dimensional Banach spaces. The main result states that ifX is an infinite-dimensional Banach space which has a not necessarily equivalent Cp-smooth norm and K is a compact subset of X, then X and X r K are Cp diffeomorphic. The proof relies on the construction of a “deleting path” through a nontrivial refinement of Bessaga’s incomplete-norm technique. However, norms are not at present available and the construction req...
On Best Approximations from RS-sets in Complex Banach Spaces
Institute of Scientific and Technical Information of China (English)
Chong LI
2005-01-01
The concept of an RS-set in a complex Banach Space is introduced and the problem of best approximation from an RS-set in a complex space is investigated. Results consisting of characterizations, uniqueness and strong uniqueness are established.
Integrals with values in Banach spaces and locally convex spaces
Mikusinski, Piotr
2014-01-01
The purpose of this article is to present the construction and basic properties of the general Bochner integral. The approach presented here is based on the ideas from the book The Bochner Integral by J. Mikusinski where the integral is presented for functions defined on $\\mathbb{R}^N$. In this article we present a more general and simplified construction of the Bochner integral on abstract measure spaces. An extension of the construction to functions with values in a locally convex space is ...
Murthy, S; Arunkumar, M; V. Govindan
2015-01-01
In this paper, the authors introduce and investigate the general solution and generalized Ulam-Hyers stability of a generalized n-type additive-quadratic functional equation. g(x + 2y; u + 2v) + g(x 2y; u 2v) = 4[g(x + y; u + v) + g(x y; u v)] 6g(x; u) + g(2y; 2v) + g(2y;2v) 4g(y; v) 4g(y;v) Where is a positive integer with , in Banach Space and Banach Algebras using direct and fixed point methods.
The generalized hardy operator with kernel and variable integral limits in banach function spaces
Lang J; Gogatishvill A
1999-01-01
Let we have an integral operator where and are nondecreasing functions, and are non-negative and finite functions, and is nondecreasing in , nonincreasing in and for and . We show that the integral operator where and are Banach functions spaces with -condition is bounded if and only if . Where and
Bound and periodic solutions of the Riccati equation in Banach space
Directory of Open Access Journals (Sweden)
A. Ya. Dorogovtsev
1995-01-01
Full Text Available An abstract, nonlinear, differential equation in Banach space is considered. Conditions are presented for the existence of bounded solutions of this equation with a bounded right side, and also for the existence of stationary (periodic solutions of this equation with a stationary (periodic process in the right side.
Known results and open problems on C1 linearization in Banach spaces
Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan
2012-01-01
The purpose of this paper is to review the results obtained by the authors on linearization of dynamical systems in infinite dimen- sional Banach spaces, especially in the C 1 case, and also to present some open problems that we believe that are still important for the understanding of the theory.
Common Fixed Point Theorems in Non-normal Cone Metric Spaces with Banach Algebras
Institute of Scientific and Technical Information of China (English)
HUANG Hua-ping; XU Shao-yuan; LIU Qiu-hua; MING Wei
2016-01-01
In this paper, we obtain a class of common fixed point theorems for generalized Lipschitz mappings in cone metric spaces with Banach algebras without the assumption of normality of cones. The results greatly generalize some results in the literature. Moreover, we give an example to support the main assertions.
Directory of Open Access Journals (Sweden)
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.
POSITIVE SOLUTIONS TO SEMI-LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACE
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.
Viscosity Approximation Method for Infinitely Many Asymptotically Nonexpansive Maps in Banach Spaces
Institute of Scientific and Technical Information of China (English)
Ruo Feng RAO
2011-01-01
In the framework of reflexive Banach spaces satisfying a weakly continuous duality map,the author uses the viscosity approximation method to obtain the strong convergence theorem for iterations with infinitely many asymptotically nonexpansive mappings.The main results obtained in this paper improve and extend some recent results.
Institute of Scientific and Technical Information of China (English)
曾六川
2003-01-01
A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced, which includes a number of known classes of nonlinear Lipschitzian mappings and non-Lipschitzian mappings in Banach spaces as special cases; for example,the known classes of nonexpansive mappings, asymptotically nonexpansive mappings and asymptotically nonexpansive type mappings. The convergence problem of modified Ishikawa iterative sequences with errors for approximating fixed points of almost asymptotically nonexpansive type mappings is considered. Not only S. S. Chang' s inequality but also H.K. Xu' s one for the norms of Banach spaces are applied to make the error estimate between the exact fixed point and the approximate one. Moreover, Zhang Shi-sheng ' s method (Applied Mathematics and Mechanics ( English Edition ), 2001,22 (1) :25 - 34) for making the convergence analysis of modified Ishikawa iterative sequences with errors is extended to the case of almost asymptotically nonexpansive type mappings. The new convergence criteria of modified Ishikawa iterative sequences with errors for finding fixed points of almost asymptotically nonexpansive type mappings in uniformly convex Banach spaces are presented. Also, the new convergence criteria of modified Mann iterative sequences with errors for this class of mappings are immediately obtained from these criteria. The above results unify, improve and generalize Zhang Shi-sheng's ones on approximating fixed points of asymptotically nonexpansive type mappings by the modified Ishikawa and Mann iterative sequences with errors.
Convergence rates for an iteratively regularized Newton–Landweber iteration in Banach space
International Nuclear Information System (INIS)
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)
Non-expansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces
Institute of Scientific and Technical Information of China (English)
Hai Yun ZHOU
2004-01-01
In this article, we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces. The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.
Institute of Scientific and Technical Information of China (English)
Wan-sheng WANG; Shou-fu LI; Run-sheng YANG
2012-01-01
A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.
Fixed point iterations for quasi-contractive maps in uniformly smooth Banach spaces
International Nuclear Information System (INIS)
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
Approximate Fixed Point Theorems in Banach Spaces with Applications in Game Theory
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.
Asymptotic behaviour of the solutions of Schroedinger equation with impulse effect in a Banach space
International Nuclear Information System (INIS)
The present paper studies the asymptotic behaviour of the solutions of linear homogeneous differential Schroedinger equation with impulse effect in a Banach space and finds a dependence between their asymptotic behaviour and the spectrum of the linear Hamiltonian operator. 6 refs
A RANDOM FIXED POINT ITERATION FOR THREE RANDOM OPERATORS ON UNIFORMLY CONVEX BANACH SPACES
Institute of Scientific and Technical Information of China (English)
Binayak S. Choudhury
2003-01-01
In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extension of a known theorem in the corresponding non-random case.
On common fixed points of compatible mappings in metric and Banach spaces
Directory of Open Access Journals (Sweden)
M. S. Khan
1988-06-01
Full Text Available We prove a number of results concerning the existence of common fixed points of a family of maps satisfying certain contractive conditions in metric and Banach spaces. Results dealing with the stucture of the set of common fixed points of such maps are also given. Our work is an improvement upon the previously known results.
The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces
Directory of Open Access Journals (Sweden)
Rabian Wangkeeree
2012-01-01
Full Text Available We introduce the general iterative methods for finding a common fixed point of asymptotically nonexpansive semigroups which is a unique solution of some variational inequalities. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature.
Strong Convergence Theorems for Strict Pseudocontractions in Uniformly Convex Banach Spaces
Directory of Open Access Journals (Sweden)
Lin Wei-Wei
2010-01-01
Full Text Available The viscosity approximation methods are employed to establish strong convergence theorems of the modified Mann iteration scheme to -strict pseudocontractions in -uniformly convex Banach spaces with a uniformly Gâteaux differentiable norm. The main result improves and extends many nice results existing in the current literature.
Some G-M-type Banach spaces and K-groups of operator algebras on them
Institute of Scientific and Technical Information of China (English)
ZHONG Huaijie; CHEN Dongxiao; CHEN Jianlan
2004-01-01
By providing several new varieties of G-M-type Banachspaces according to decomposable and compoundable properties, this paper discusses the operator structures of thesespaces and the K-theory of the algebra of the operators on these G-M-type Banach spaces throughcalculation of the K-groups of the operator ideals contained in the class of Riesz operators.
Psi-exponential dichotomy for linear differential equations in a Banach space
Directory of Open Access Journals (Sweden)
Atanaska Georgieva
2013-07-01
Full Text Available In this article we extend the concept psi-exponential and psi-ordinary dichotomies for homogeneous linear differential equations in a Banach space. With these two concepts we prove the existence of psi-bounded solutions of the appropriate inhomogeneous equation. A roughness of the psi-dichotomy is also considered.
Nonuniform Exponential Stability and Instability of Evolution Operators in Banach Space
Mihaela Tomescu; Andrea Minda
2006-01-01
In this paper is presenting a parallel between nonuniform exponential stability and nonuniform exponential instability of evolution operators in Banach spaces, beginning to present the concept of the evolution operator with nonuniform exponential decay, respectively growth, next with the concept of the nonuniform stability, respectively instability, nonuniform exponential stability, respectively instability, nonuniform integrable stability, respectively instability and...
Nonuniform Exponential Stability and Instability of Evolution Operators in Banach Space
Directory of Open Access Journals (Sweden)
Mihaela Tomescu
2006-10-01
Full Text Available In this paper is presenting a parallel between nonuniform exponential stability and nonuniform exponential instability of evolution operators in Banach spaces, beginning to present the concept of the evolution operator with nonuniform exponential decay, respectively growth, next with the concept of the nonuniform stability, respectively instability, nonuniform exponential stability, respectively instability, nonuniform integrable stability, respectively instability and relationship between this concepts.
Convergence to Compact Sets of Inexact Orbits of Nonexpansive Mappings in Banach and Metric Spaces
Directory of Open Access Journals (Sweden)
2009-02-01
Full Text Available We study the influence of computational errors on the convergence to compact sets of orbits of nonexpansive mappings in Banach and metric spaces. We first establish a convergence theorem assuming that the computational errors are summable and then provide examples which show that the summability of errors is necessary for convergence.
ASYMPTOTICALLY ISOMETRIC COPIES OF lp (1≤p＜∞) AND c0 IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
Chen Dongyang
2006-01-01
Let X be a Banach space. If there exists a quotient space of X which is asymptotically isometric to l1, then X contains complemented asymptotically isometric copies of l1. Every infinite dimensional closed subspace of l1 contains a complemented subspace of l1 which is asymptotically isometric to l1. Let X be a separable Banach space such that X* contains asymptotically isometric copies of lp (1 ＜ p ＜∞). Then there exists a quotient space of X which is asymptotically isometric to lq (1/p+1/q=1). Complementedasymptotically isometric copies of c0 in K(X, Y) and W(X, Y) are discussed. Let X be a Gelfand-Phillips space. If X contains asymptotically isometric copies of c0, it has to contain complemented asymptotically isometric copies of c0.
Directory of Open Access Journals (Sweden)
N. L. Braha
2005-05-01
Full Text Available In this paper we will give a characterization of 1-absolutely summing operators using μ-approximate l_1 sequences. Exactly if (x_n _1^∞ is μ-approximate l_1 , basic and normalized sequence in Banach space X then every bounded linear operator T from X into Banach space Y is 1-absolutely summing if and only if Y is isomorphic to Hilbert space.
On well posedness of best simultaneous approximation problems in Banach spaces
Institute of Scientific and Technical Information of China (English)
LI; Chong
2001-01-01
［1］Pinkus, A., Uniqueness in vector-valued approximation, J. Approx. Theory, 1993, 73: 17—92.［2］Li, C., Watson, G. A., On best simultaneous approximation, J. Approx. Theory, 1997, 91: 332—348.［3］Tanimoto, S., A characterization of best simultaneous approximations, J. Approx. Theory, 1989, 59: 359—361.［4］Watson, G. A., A characterization of best simultaneous approximations, J. Approx. Theory, 1993, 75: 175—182.［5］Li, C., Watson, G. A., On best simultaneous approximation of a finite set of functions, Computer Math. Applic., 1999, 37: 1—9.［6］Stechkin, S. B., Approximation properties of sets in normed linear spaces, Rev. Roumaine Math. Pures and Appl. (in Russian), 1963, 8: 5—18.［7］Borwein, J. M., Fitzpatrick, S., Existence of nearest points in Banach spaces, Can. J. Math., 1989, 41: 702—720.［8］De Blasi, F. S., Myjak, J., On a generalized best approximation problem, J. Approx. Theory, 1998, 94: 54—72.［9］Georgiev, P. G., The strong Ekeland variational principle, the strong drop theorem and applications, J. Math. Anal. Appl., 1988, 131: 1—21.［10］Lau, K. S., Almost Chebyshev subsets in reflexive Banach spaces, Indiana Univ. Math. J., 1978, 27: 791—795.［11］Li, C., On mutually nearest and mutually furthest points in reflexive Banach spaces, J. Approx. Theory, 2000, 103: 1—17.［12］Li, C., On well posed generalized best approximation problems, J. Approx. Thory, 2000, 107: 96—108.［13］Li, C., Almost K-Chebyshev sets, Acta. Math. Sin. (in Chinese), 1990, 33: 251—259.［14］De Blasi, F. S., Myjak, J., Papini, P. L., On mutually nearest and mutually furthest points of sets in Banach spaces, J. Approx. Theory, 1992, 70: 142—155.［15］Dontchev, A., Zolezzi, T., Well Posed Optimization Problems, Lecture Notes in Math., Vol. 1543, New York: Springer-Verlag, 1993.［16］Li, C., Wang, X. H., Almost Chebyshev set with respect to bounded subsets, Science in China, Ser. A, 1997, 40: 375—383.［17］Ni, R
Institute of Scientific and Technical Information of China (English)
Boulbeba Abdelmoumen; Aref Jeribi; Maher Mnif
2012-01-01
In this paper,we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness.Moreover,we apply the obtained results to discuss the incidence of some perturbation results realized in [2] on the behavior of essential spectra of such closed densely defined linear operators on Banach spaces.These results are exploited to investigate the essential spectra of a multidimensional neutron transport operator on L1 spaces.
Domains of uniqueness for $C_0$-semigroups on the dual of a Banach space
Lemle, Ludovic Dan
2008-01-01
Let $({\\cal X},\\|\\:.\\:\\|)$ be a Banach space. In general, for a $C_0$-semigroup \\semi on $({\\cal X},\\|\\:.\\:\\|)$, its adjoint semigroup \\semia is no longer strongly continuous on the dual space $({\\cal X}^{*},\\|\\:.\\:\\|^{*})$. Consider on ${\\cal X}^{*}$ the topology of uniform convergence on compact subsets of $({\\cal X},\\|\\:.\\:\\|)$ denoted by ${\\cal C}({\\cal X}^{*},{\\cal X})$, for which the usual semigroups in literature becomes $C_0$-semigroups.\\\\ The main purpose of this paper is to prove th...
M. B. Ghaemi; H. Majani; Cho, Y J; Eshaghi Gordji, M.
2011-01-01
Using the fixed point method, we investigate the stability of the systems of quadratic-cubic and additive-quadratic-cubic functional equations with constant coefficients form r-divisible groups into Ŝerstnev probabilistic Banach spaces.
Linear embeddings of finite-dimensional subsets of Banach spaces into Euclidean spaces
International Nuclear Information System (INIS)
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, dH(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 > 2dB(X). A related argument shows that if the Assouad dimension of X − X is finite and k > dA(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)
Banach空间中的Xd Bessel列%Sequences of Xd Bessel for a Banach space
Institute of Scientific and Technical Information of China (English)
王亚丽; 曹怀信; 张巧卫
2011-01-01
研究了Banach空间X中的Xd Bessel列、Xd框架、Xd独立框架、Xd紧框架与Xd Riesz基.证明了当Xd为BK-空间时,(BXXd,‖·‖)是数域F上的Banach空间；当Xd是BK-空间且X自反时,通过定义算子Tf,建立了空间BXXd与算子空间B(X*,Xd)之间的等距同构,为利用算子论的方法研究Xd Bessel列提供了必要的理论依据.最后,给出了Banach空间X中Xd Bessel列的等价刻画并证明了独立的Xd框架与Xd Riesz基是一致的.%Xd Bessel sequences, Xd frames, Xd independent frames, Xd tight frames and Xd Riesz basis for a Banach space X ate introduced and discussed. It is proved that (Bxxd || ? || ) is a Banach space when Xd is a BK-space. By de fining an operator Tf, an isometric isomorphism from Bxxd to B(X* ,Xd) is established when Xd is a BK-space and X is reflexive, which provides a necessary theoretical basis for studying Xd Bessel sequences by the operator theory. Finally, the equivalent characterizations of Xd Bessel sequences for a Banach space X are given. Also, it is proved that independ ent Xd frames and Xd Riesz bases for a Banach space X are the same.
Additive maps preserving the reduced minimum modulus of Banach space operators
Bourhim, Abdellatif
2009-01-01
Let ${\\mathcal B}(X)$ be the algebra of all bounded linear operators on an infinite dimensional complex Banach space $X$. We prove that an additive surjective map $\\phi$ on ${\\mathcal B}(X)$ preserves the reduced minimum modulus if and only if either there are bijective isometries $U:X\\to X$ and $V:X\\to X$ both linear or both conjugate linear such that $\\phi(T)=UTV$ for all $T\\in{\\mathcal B}(X)$, or $X$ is reflexive and there are bijective isometries $U:X^*\\to X$ and $V:X\\to X^*$ both linear or both conjugate linear such that $\\phi(T)=UT^*V$ for all $T\\in{\\mathcal B}(X)$. As immediate consequences of the ingredients used in the proof of this result, we get the complete description of surjective additive maps preserving the minimum, the surjectivity and the maximum moduli of Banach space operators.
Inexact Newton–Landweber iteration for solving nonlinear inverse problems in Banach spaces
International Nuclear Information System (INIS)
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)
Cauchy-Rassias Stability of Cauchy-Jensen Additive Mappings in Banach Spaces
Institute of Scientific and Technical Information of China (English)
Choonkil BAAK
2006-01-01
Let X, Y be vector spaces. It is shown that if a mapping f: X → Y satisfiesf(x+y/2+z)+f(x-y/2+z)=f(x)+2f(z), (0.1)f(x+y/2+z)-f(x-y/2+z)= f(y), (0.2)or2f(x+y/2+z)=f(x)+f(y)+2f(z) (0.3)for all x, y, z ∈ X, then the mapping f: X → Y is Cauchy additive.Furthermore, we prove the Cauchy-Rassias stability of the functional equations (0.1), (0.2) and (0.3) in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebra.
Common Fixed-Point Problem for a Family Multivalued Mapping in Banach Space
Directory of Open Access Journals (Sweden)
Zhanfei Zuo
2011-01-01
Full Text Available It is our purpose in this paper to prove two convergents of viscosity approximation scheme to a common fixed point of a family of multivalued nonexpansive mappings in Banach spaces. Moreover, it is the unique solution in to a certain variational inequality, where ∶=∩∞=0( stands for the common fixed-point set of the family of multivalued nonexpansive mapping {}.
Mann Type Implicit Iteration Approximation for Multivalued Mappings in Banach Spaces
Directory of Open Access Journals (Sweden)
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.
Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces
Jong Soo Jung
2008-01-01
Abstract Let be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of has the fixed point property for nonexpansive mappings. Let be a nonempty closed convex subset of , a contractive mapping (or a weakly contractive mapping), and nonexpansive mapping with the fixed point set . Let be generated by a new composite iterative scheme: , , . It is proved that converges strongly to a point in , which is a s...
Tomonari Suzuki
2006-01-01
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 .
Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces
Saeidi Shahram
2008-01-01
Abstract Let be a left amenable semigroup, let be a representation of as Lipschitzian mappings from a nonempty compact convex subset of a smooth Banach space into with a uniform Lipschitzian condition, let be a strongly left regular sequence of means defined on an -stable subspace of , let be a contraction on , and let , , and be sequences in (0, 1) such that , for all . Let , for all . Then, under suitable hypotheses on the constants, we show that converges stron...
Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces
Directory of Open Access Journals (Sweden)
Yongjin Li
2013-08-01
Full Text Available We prove the Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces. That is, if y is an approximate solution of the differential equation $y''+ alpha y'(t +eta y = 0$ or $y''+ alpha y'(t +eta y = f(t$, then there exists an exact solution of the differential equation near to y.
Nonlinear Evolution Governed by Accretive Operators in Banach Spaces: Error Control and Applications
Nochetto, Ricardo H; Savare, Giuseppe
2001-01-01
Nonlinear evolution equations governed by $m$-accretive operators in Banach spaces are discretized via the backward or forward Euler methods with variable stepsize. Computable a posteriori error estimates are derived in terms of the discrete solution and data, and shown to converge with optimal order $O(sqrttau)$. Applications to scalar conservation laws and degenerate parabolic equations (with or without hysteresis) in $L^1$, as well as to Hamilton-Jacobi equations in $C^...
MIXED MONOTONE ITERATIVE TECHNIQUES FOR SEMILINEAR EVOLUTION EQUATIONS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
王良龙; 王志成
2004-01-01
This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.
Fixed point iterations for strictly hemi-contractive maps in uniformly smooth Banach spaces
International Nuclear Information System (INIS)
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)
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 .
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
Directory of Open Access Journals (Sweden)
Erzakova Nina A
2004-01-01
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.
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.
Hierarchy of Hamilton equations on Banach Lie-Poisson spaces related to restricted Grassmannian
Golinski, Tomasz
2009-01-01
Using the Magri method one defines an involutive family of Hamiltonians on Banach Lie-Poisson space iR+UL_res^1 (which contains the restricted Grassmannian as a symplectic leaf) and on its complexification C+L_res^1. The hierarchy of Hamilton equations given by these Hamiltonians is investigated. The operator equations of Ricatti-type are included in this hierarchy. For a few particular cases one gives the explicit solutions.
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. 79-97. 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: 0.951, year: 2014 http://www. science direct.com/ science /article/pii/S0021904516000265
A reinterpretation of set differential equations as differential equations in a Banach space
Rasmussen, Martin; Rieger, Janosch; Webster, Kevin
2015-01-01
Set differential equations are usually formulated in terms of the Hukuhara differential, which implies heavy restrictions for the nature of a solution. We propose to reformulate set differential equations as ordinary differential equations in a Banach space by identifying the convex and compact subsets of $\\R^d$ with their support functions. Using this representation, we demonstrate how existence and uniqueness results can be applied to set differential equations. We provide a simple example,...
Institute of Scientific and Technical Information of China (English)
LI Shoufu
2005-01-01
A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.
Weak and Strong Convergence Theorems for Nonexpansive Mappings in Banach Spaces
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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.
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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.
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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.
Hytonen, Tuomas; van Neerven, Jan; Portal, Pierre
2007-01-01
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-McIntosh-Russ, the tent spaces in turn are used to construct a scale of vector-valued Hardy spaces associated with a given bisectorial operator (A) with certain off-diagonal bounds, such that (A) always has a bounded (H^{\\infty})-functional calculus on these spaces. This provides a new way of proving functional ...
On Linear Isometries of Banach Lattices in $\\mathcal{C}_0()$-Spaces
Indian Academy of Sciences (India)
José M Isidro
2009-11-01
Consider the space $\\mathcal{C}_0()$ endowed with a Banach lattice-norm $\\|\\cdot p\\|$ that is not assumed to be the usual spectral norm $\\|\\cdot p\\|_∞$ of the supremum over . A recent extension of the classical Banach-Stone theorem establishes that each surjective linear isometry of the Banach lattice $(\\mathcal{C}_0(),\\|\\cdot p\\|)$ induces a partition of into a family of finite subsets $S\\subset$ along with a bijection $T:→$ which preserves cardinality, and a family $[u(S):S\\in]$ of surjective linear maps $u(S):\\mathcal{C}(T(S))→\\mathcal{C}(S)$ of the finite-dimensional *-algebras $\\mathcal{C}(S)$ such that $$(U f)|_{T(S)}=u(S)(f|_S) \\quad \\forall f\\in\\mathcal{C}_0() \\quad \\forall S\\in.$$ Here we endow the space of finite sets $S\\subset$ with a topology for which the bijection and the map are continuous, thus completing the analogy with the classical result.
Casazza, Peter G.; Christensen, Ole
1995-01-01
We prove that a Hilbert space frame $\\fti$ contains a Riesz basis if every subfamily $\\ftj , J \\subseteq I ,$ is a frame for its closed span. Secondly we give a new characterization of Banach spaces which do not have any subspace isomorphic to $c_0$. This result immediately leads to an improvement of a recent theorem of Holub concerning frames consisting of a Riesz basis plus finitely many elements.
Fixed Point Theorems for Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces
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Abkar A
2010-01-01
Full Text Available In the first part of this paper, we prove the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space. In this way, we generalize the result of Dhompongsa et al. (2006. In the second part of this paper, we prove a fixed point theorem for upper semicontinuous mappings satisfying the Suzuki condition in strictly spaces; our result generalizes a recent result of Domínguez-Benavides et al. (2009.
Convergence rates for the iteratively regularized Gauss–Newton method in Banach spaces
International Nuclear Information System (INIS)
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
Delta-semidefinite and delta-convex quadratic forms in Banach spaces
Kalton, N.; Konyagin, S. V.; Vesely, L.
2006-01-01
A continuous quadratic form ("quadratic form", in short) on a Banach space $X$ is: (a) delta-semidefinite (i.e., representable as a difference of two nonnegative quadratic forms) if and only if the corresponding symmetric linear operator $T\\colon X\\to X^*$ factors through a Hilbert space; (b) delta-convex (i.e., representable as a difference of two continuous convex functions) if and only if $T$ is a UMD-operator. It follows, for instance, that each quadratic form on an infinite-dimensional $...
Existence results for a class of parabolic evolution equations in Banach spaces
Institute of Scientific and Technical Information of China (English)
WangJing; XueXingmei
2003-01-01
We discuss the existence results of the parabolic evolution equation d(x(t) + g(t,x(t)))/dt + A(t)x(t) =f( t ,x(t)) in Banach spaces, where A (t) generates an evolution system and functions f, g are continuous. We get the theorem of existence of a mild solution, the theorem of existence and uniqueness of a mild solution and the theorem of existence and uniqueness of an S-classieal (semi-classical) solution. We extend the cases when g(t) = 0 or A(t) = A.
Some compactness tests in Banach spaces by Cesaro means of Fourier coefficients
Öztürk, Seda
2015-09-01
Let H be a complex Banach space, T be the topological group of the unit circle with respect to the Euclidean topology, α be a strongly continuous isometric linear representation of T in H, {Fkα}k ∈ℤ be the family of Fourier coefficients with respect to α, and {σkα}k ∈ℤ be Cesaro means of the family {Fkα}k ∈ℤ . In this work, we give some compactness tests for closed subsets of H.
Oscillation and the mean ergodic theorem for uniformly convex Banach spaces
Avigad, Jeremy; Rute, Jason
2012-01-01
Let B be a p-uniformly convex Banach space, with p >= 2. Let T be a linear operator on B, and let A_n x denote the ergodic average (1 / n) sum_{i< n} T^n x. We prove the following variational inequality in the case where T is power bounded from above and below: for any increasing sequence (t_k)_{k in N} of natural numbers we have sum_k || A_{t_{k+1}} x - A_{t_k} x ||^p
ANTI-PERIODIC SOLUTIONS FOR FIRST AND SECOND ORDER NONLINEAR EVOLUTION EQUATIONS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
WEI Wei; XIANG Xiaoling
2004-01-01
In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presentedThe equations con-tain nonlinear monotone operators and a nonmonotone perturbationMoreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of second-order nonlinear evolution equations is verifiedOur abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.
Approximation of fixed points of Lipschitz pseudo-contractive mapping in Banach spaces
International Nuclear Information System (INIS)
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
Existence of Solutions to Nonlinear Impulsive Volterra Integral Equations in Banach Spaces
Institute of Scientific and Technical Information of China (English)
CHEN Fangqi; TIAN Ruilan
2005-01-01
In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R+ in Banach spaces.By the use of a new comparison result and recurrence method, the new existence theorems are achieved under a weaker compactness-type condition, which generalize and improve the related results for this class of equations with finite moments of impulse effect on finite interval and infinite moments of impulse effect on infinite interval.
Basic Properties of Banach Space Xμ%Banach空间Xμ的基本性质
Institute of Scientific and Technical Information of China (English)
郑列
2005-01-01
研究了Banach空间Xμ={c=(ci)i≥1:‖c‖μ=def ∞∑ i=1 iμ|Ci|∞},μ≥1.讨论了它的范数,紧性以及强收敛和弱收敛之间的关系.%Banach space Xμ= {c= (ci)i≥1: ‖c‖μ=def ∞∑ i=1 iμ|ci|∞},μ≥1. is studied. Our results relate to norm,compactness and the relation between strong convergence and weak * convergence.
Convergence theorems for a class of nonlinear maps in uniformly smooth Banach spaces
International Nuclear Information System (INIS)
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.
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.
Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces
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Udomene Aniefiok
2006-01-01
Full Text Available Suppose is a nonempty closed convex subset of a real Banach space . Let be two asymptotically quasi-nonexpansive maps with sequences such that and , and . Suppose is generated iteratively by where and are real sequences in . It is proved that (a converges strongly to some if and only if ; (b if is uniformly convex and if either or is compact, then converges strongly to some . Furthermore, if is uniformly convex, either or is compact and is generated by , where , are bounded, are real sequences in such that and , are summable; it is established that the sequence (with error member terms converges strongly to some .
C0-semigroups of linear operators on some ultrametric Banach spaces
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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.
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.
Local subdifferentials and multivariational inequalities in Banach and Frechet spaces
Pavlo O. Kasyanov; Valery S. Mel'nik; Anna M. Piccirillo
2008-01-01
Some functional-topological concepts of subdifferential and locally subdifferential maps in Frechet spaces are established. Multivariational inequalities with an operator of the pseudo-monotone type, connected with subdifferential maps, are considered.
On growth and covering theorems of quasi-convex mappings in the unit ball of a complex Banach space
Institute of Scientific and Technical Information of China (English)
ZHANG; Wenjun(张文俊); LIU; Taishun(刘太顺)
2002-01-01
A class of biholomorphic mappings named "quasi-convex mapping" is introduced in the unitball of a complex Banach space. It is proved that this class of mappings is a proper subset of the class ofstarlike mappings and contains the class of convex mappings properly, and it has the same growth and coveringtheorems as the convex mappings. Furthermore, when the Banach space is confined to Cn, the "quasi-convexmapping" is exactly the "quasi-convex mapping of type A" introduced by K. A. Roper and T. J. Suffridge.
Isomorphisms on weighed Banach spaces of harmonic and holomorphic functions
Jorda Mora, Enrique; ZARCO GARCIA, ANA MARIA
2013-01-01
For an arbitrary open subset U subset of R-d or U subset of C-d and a continuous function v : U ->]0,infinity[ we show that the space h(v0) (U) of weighed harmonic functions is almost isometric to a (closed) subspace of c(0), thus extending a theorem due to Bonet and Wolf for spaces of holomorphic functions H-v0 (U) on open sets U subset of C-d. Inspired by recent work of Boyd and Rueda, we characterize in terms of the extremal points of the dual of h(v0) (U) when h(v0) (U) is isometric to a ...
A convergence rates result for an iteratively regularized Gauss–Newton–Halley method in Banach space
International Nuclear Information System (INIS)
The use of second order information on the forward operator often comes at a very moderate additional computational price in the context of parameter identification problems for differential equation models. On the other hand the use of general (non-Hilbert) Banach spaces has recently found much interest due to its usefulness in many applications. This motivates us to extend the second order method from Kaltenbacher (2014 Numer. Math. at press), (see also Hettlich and Rundell 2000 SIAM J. Numer. Anal. 37 587620) to a Banach space setting and analyze its convergence. We here show rates results for a particular source condition and different exponents in the formulation of Tikhonov regularization in each step. This includes a complementary result on the (first order) iteratively regularized Gauss–Newton method in case of a one-homogeneous data misfit term, which corresponds to exact penalization. The results clearly show the possible advantages of using second order information, which get most pronounced in this exact penalization case. Numerical simulations for an inverse source problem for a nonlinear elliptic PDE illustrate the theoretical findings. (paper)
Institute of Scientific and Technical Information of China (English)
Shi-sheng ZHANG
2009-01-01
The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper investigates the existence and multiplicity of nonnegative solutions to a singular nonlinear boundary value problem of second order differential equations with integral boundary conditions in a Banach space. The arguments are based on the construction of a nonempty bounded open convex set and fixed point index theory. Our nonlinearity possesses singularity and first derivative which makes it different with that in [10].
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Rongfei Lin
2013-01-01
Full Text Available Newton-Kantorovich and Smale uniform type of convergence theorem of a deformed Newton method having the third-order convergence is established in a Banach space for solving nonlinear equations. The error estimate is determined to demonstrate the efficiency of our approach. The obtained results are illustrated with three examples.
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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.
On Well-posed Mutually Nearest and Mutually Furthest Point Problems in Banach Spaces
Institute of Scientific and Technical Information of China (English)
Chong LI; Ren Xing NI
2004-01-01
Let G be a non-empty closed (resp. bounded closed) boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X. Let K(X) denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance. Moreover, let KG(X) denote the closure of the set {A ∈ K(X): A∩G =φ}. We prove that the set of all A ∈KG(X) (resp. A ∈ K(X)), such that the minimization (resp. maximization) problem min(A, G) (resp. max(A, G)) is well posed, contains a dense Gδ-subset of KG(X) (resp. K(X)), thus extending the recent results due to Blasi, Myjak and Papini and Li.
Models of CT dose profiles in Banach space; with applications to CT Dosimetry
Weir, Victor J
2015-01-01
This paper consists of two parts.In the first part, the scatter components of computed tomograpahy dose profiles are modeled using various functions including the solution to Riccati's differential equation. These scatter functions are combined with primary components such as a trapezoidal function and a constructed function that uses the analytic continuation of Heaviside step function. A mathematical theory is developed in Banach space. The modeled function, which is the product of the scatter and primary functions, is used to accurately fit data from the O-arm cone beam imaging system. In a second part of the paper, an approach to dosimtery is developed that shows that the results obtained from the use of a pencil shaped ion chamber is equivalent to that from a farmer chamber. This result is verified by presenting some preliminary experimental data measured in a 64 slice Siemens Sensation scanner.
A Banach space-valued ergodic theorem for amenable groups and applications
Pogorzelski, Felix
2012-01-01
In this paper we study unimodular amenable groups. The first part is devoted to results on the existence of uniform families of quasi tilings for these groups. In light of that, constructions of Ornstein and Weiss are extended by quantitative estimates for the covering properties of the corresponding decompositions. Afterwards, we apply the developed methods to obtain an abstract ergodic theorem for a class of functions mapping subsets of the group into some Banach space. Moreover, applications of this convergence result are studied: the uniform existence of the integrated density of states (IDS) for operators on amenable Cayley graphs; the uniform existence of the IDS for operators on discrete structures being quasi-isometric to some amenable group; the approximation of L2-Betti numbers on cellular CW-complexes; the existence of certain densities of clusters in a percolated Cayley graph.
International Nuclear Information System (INIS)
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
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
Improved bounds in the scaled Enflo type inequality for Banach spaces
Giladi, Ohad
2010-01-01
It is shown that if (X,||.||_X) is a Banach space with Rademacher type p \\ge 1, then for every integer n there exists an even integer m X, \\Avg_{x,\\e}[||f(x+ m\\e/2)-f(x)}||_X^p] < C(p,X) m^p\\sum_{j=1}^n\\Avg_x[||f(x+e_j)-f(x)||_X^p], where the expectation is with respect to uniformly chosen x \\in Z_m^n and \\e \\in \\{-1,1\\}^n, and C(p,X) is a constant that depends on p and the Rademacher type constant of X. This improves a bound of m < Cn^{3-2/p} that was obtained in [Mendel, Naor 2007]. The proof is based on an augmentation of the "smoothing and approximation" scheme, which was implicit in [Mendel, Naor 2007].
Song, Guohui; Zhang, Haizhang
2011-01-01
A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space that satisfies the linear representer theorem brings the advantage of discarding the hypothesis error from the sum automatically. Following this direction, we illustrate how reproducing kernel Banach spaces with the l1 norm can be applied to improve the learn...
Strong convergence theorems for uniformly L-Lipschitzian mappings in Banach spaces
International Nuclear Information System (INIS)
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 {αn}n≥0 and {γn}n≥0 subset of (0, 1) be such that limn→∞ αn = 0 = limn→ ∞ γn and limn→ ∞(βn - 1)/ αn = 0, where βn Σj=0n λj and λj = 1 + αjγjL. Let Sn := (1 - αnγn)I + αnγnTn. It is proved that there exists some integer N0 > 1, such that for each n ≥ N0, there exists unique xn element of K such that xn = αnu+(1 -αn) 1/ (n + 1) Σj=0n Sjxn. If φ : E → R is defined by φ (y) := LIMn vertical bar vertical bar xn -y vertical bar vertical bar2 for all y element of E here LIM denotes a Banach limit, vertical bar vertical bar xn - Txn vertical bar vertical bar → 0 as n → ∞ and Kmin intersection F (T) ≠ 0, where Kmin := {x element of E : φ (x) = min (u element of K) φ (u) }, then it is proved that {xn} converges strongly to a fixed point of T. As an application, it is proved that the iterative process, z0 element of K, zn+1 alpha#nu + (1 - αn) 1/ (n + 1) Σj=0n Sjzn , n ≥ 0, under suitable conditions on the iteration parameters, converges strongly to a fixed point of T. (author)
Perturbations of Bessel Sequences of Order p in a Banach Space%Banach空间中P阶Bessel列的扰动
Institute of Scientific and Technical Information of China (English)
王秋芬; 曹怀信; 武海辉
2011-01-01
应用算子论方法研究Banach空间X中p(1＜P＜∞)阶Bessel列的扰动问题,对X中的任一p阶Bessel列f={fi}i∈I,定义了有界线性算子Tf:X*→lp,建立了从全体p阶Bessel列组成的Banach空间BpX(Ⅰ)到算子空间B(X*,lp)上的等距线性同构α:f→Tf,并给出了p阶Bessel列的扰动定理.%With the aid of operator theory, some perturbations of Bessel sequences of order p in a Banach space X were discussed. For a Bessel sequence f = {fi} i∈I of order p in X, we defined a bounded linear operator Tf from X* into lp and established a linear isometry isomorphism a from the space BpX (I) of all the Bessel sequences of order p in a Banach space X into the operator space B(X*,lp) defined by α(f) = Tr. In the light of operator theory, some results on perturbations of Bessel sequences of order p were given, which are helpful to the study of frames of order p for a Banach space.
Quasi-geostrophic equations with initial data in Banach spaces of local measures
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Sadek Gala
2005-06-01
Full Text Available This paper studies the well posedness of the initial value problem for the quasi-geostrophic type equations $$displaylines{ partial_{t}heta+u ablaheta+( -Delta ^{gamma}heta =0 quad hbox{on }mathbb{R}^{d}imes] 0,+infty[cr heta( x,0 =heta_{0}(x, quad xinmathbb{R}^{d} }$$ where 0 less than $gammaleq 1$ is a fixed parameter and the velocity field $u=(u_{1},u_{2},dots,u_{d} $ is divergence free; i.e., $ abla u=0$. The initial data $heta_{0}$ is taken in Banach spaces of local measures (see text for the definition, such as Multipliers, Lorentz and Morrey-Campanato spaces. We will focus on the subcritical case 1/2 less than $gammaleq1$ and we analyse the well-posedness of the system in three basic spaces: $L^{d/r,infty}$, $dot {X}_{r}$ and $dot {M}^{p,d/r}$, when the solution is global for sufficiently small initial data. Furtheremore, we prove that the solution is actually smooth. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions.
Sokhuma, K.; A. Kaewkhao
2010-01-01
Let be a nonempty compact convex subset of a uniformly convex Banach space , and let and be a single-valued nonexpansive mapping and a multivalued nonexpansive mapping, respectively. Assume in addition that and for all . We prove that the sequence of the modified Ishikawa iteration method generated from an arbitrary by , , where and , are sequences of positive numbers satisfying , , converges strongly to a common fixed point of and ; that is, there exists such tha...
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M. Eshaghi Gordji
2009-01-01
Full Text Available We establish the general solution of the functional equation f(nx+y+f(nx−y=n2f(x+y+n2f(x−y+2(f(nx−n2f(x−2(n2−1f(y for fixed integers n with n≠0,±1 and investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces.
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Vara Prasad KNVV
2006-01-01
Full Text Available Let be an arbitrary real Banach space and a nonempty, closed, convex (not necessarily bounded subset of . If is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant , then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration. It is also shown that the Mann iteration converges faster than the Ishikawa iteration to the fixed point of .
International Nuclear Information System (INIS)
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 T1, T2, . . . , Tm : K → K be asymptotically nonexpansive mappings of K into E with sequences (respectively) {kin}n=1∞ satisfying kin → 1 as n → ∞, i = 1, 2 , ...,m and Σn=1∞(kin - 1) in}n=1∞ be a sequence in [ε, 1 - ε ], for each i element of { 1, 2 , . . . ,m} (respectively). Let {xn} be a sequence generated for m ≥ 2 by, x1 element of K, xn+1 = (1 - α1n)xn + α1nT1nyn+m-2, yn+m-2 = (1 - α2n)xn + α2nT2nyn+m-3, ..., yn = (1 - αmn)xn + αmnTmnxn , n ≥ 1. Let Intersectioni=1m F (Ti) ≠ 0 . Then, {xn} converges weakly to a common fixed point of the family {Ti}i=1m. Under some appropriate condition on the family {Ti}i=1m, a strong convergence theorem is also roved. (author)
Sharp quantitative nonembeddability of the Heisenberg group into superreflexive Banach spaces
Austin, Tim; Tessera, Romain
2010-01-01
Let $\\H$ denote the discrete Heisenberg group, equipped with a word metric $d_W$ associated to some finite symmetric generating set. We show that if $(X,\\|\\cdot\\|)$ is a $p$-convex Banach space then for any Lipschitz function $f:\\H\\to X$ there exist $x,y\\in \\H$ with $d_W(x,y)$ arbitrarily large and \\begin{equation}\\label{eq:comp abs} \\frac{\\|f(x)-f(y)\\|}{d_W(x,y)}\\lesssim \\left(\\frac{\\log\\log d_W(x,y)}{\\log d_W(x,y)}\\right)^{1/p}. \\end{equation} We also show that any embedding into $X$ of a ball of radius $R\\ge 4$ in $\\H$ incurs bi-Lipschitz distortion that grows at least as a constant multiple of \\begin{equation}\\label{eq:dist abs} \\left(\\frac{\\log R}{\\log\\log R}\\right)^{1/p}. \\end{equation} Both~\\eqref{eq:comp abs} and~\\eqref{eq:dist abs} are sharp up to the iterated logarithm terms. When $X$ is Hilbert space we obtain a representation-theoretic proof yielding bounds corresponding to~\\eqref{eq:comp abs} and~\\eqref{eq:dist abs} which are sharp up to a universal constant.
International Nuclear Information System (INIS)
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 T1, T2, ..., TN be a family of nonexpansive self-mappings of K, with F := intersectioni=1N Fix(Ti) ≠ 0, F = Fix(TNTN-1... T1) = Fix(T1TN ... T2) = ... Fix(TN-1TN-2... T1TN). Let { λn} be a sequence in (0, 1) satisfying the following conditions: C1 : lim λn 0; C2 : Σ λn = ∞ . For a fixed δ element of (0, 1), define Sn : K → K by Snx := (1 - δ )x + δTnx for all x element of K where Tn = Tn mod N. For arbitrary fixed u, x0 element of K, let B := { x element of K : TNTN-1... T1x γx+(1- γ)u, for some γ > 1} be bounded and let the sequence {xn} be defined iteratively by xn+1 λn+1u + (1 - λn+1 )Sn+1xn, for n ≥ 0. Assume that lim n→∞ vertical bar vertical bar Tnxn - Tn+1 xn vertical bar vertical bar = 0. Then, {xn} converges strongly to a common fixed point of the family T1, T2, ..., TN. Convergence theorem is also proved for non-self maps. (author)
Lp-DICHOTOMY OF LINEAR DIFFERENTIAL EQUATIONS IN AN ARBITRARY BANACH SPACE
Institute of Scientific and Technical Information of China (English)
A. KOSSEVA; S. KOSTADINOV; K. SCHNEIDER
2003-01-01
The notion of Lp-dichotomy for linear differential equations with possibly unbounded oper-ator is introduced. By help of Banach fixed point theorem sufficient conditions for the existenceof bounded solutions of nonlinear differential equations with an Lp-dichotomous linear part areobtained.
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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.
Institute of Scientific and Technical Information of China (English)
Li Shan LIU
2001-01-01
In this paper, we will prove that Ky Fan's Theorem (Math. Z. 112(1969), 234-240) is true for1-set-contractive maps defined on a bounded closed convex subset K in a Banach space with intK ≠φ.This class of 1-set-contractive maps includes condensing maps, nonexpansive maps, semicontractivemaps, LANE maps and others. As applications of our theorems, some fixed point theorems of non-self-maps are proved under various well-known boundary conditions. Our results are generalizations andimprovements of the recent results obtained by many authors.
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K. N. V. V. Vara Prasad
2007-01-01
Full Text Available Let E be an arbitrary real Banach space and K a nonempty, closed, convex (not necessarily bounded subset of E. If T is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant LÃ¢Â‰Â¥1, then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration. It is also shown that the Mann iteration converges faster than the Ishikawa iteration to the fixed point of T.
Ring homomorphisms on real Banach algebras
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Sin-Ei Takahasi
2003-08-01
Full Text Available Let B be a strictly real commutative real Banach algebra with the carrier space ÃŽÂ¦B. If A is a commutative real Banach algebra, then we give a representation of a ring homomorphism ÃÂ:AÃ¢Â†Â’B, which needs not be linear nor continuous. If A is a commutative complex Banach algebra, then ÃÂ(A is contained in the radical of B.
International Nuclear Information System (INIS)
In this paper we investigate the relation between weak convergence of a sequence {μn} of probability measures on a Polish space S converging weakly to the probability measure μ and continuous, norm-bounded functions into a Banach space X. We show that, given a norm-bounded continuous function f:S→X, it follows that limn∞ ∫Sf, dμn = ∫Sf, dμ —the limit one has for bounded and continuous real (or complex)—valued functions on S. This result is then applied to the stability theory of Feynman’s operational calculus where it is shown that the theory can be significantly improved over previous results.
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D. A. Robbins
1994-12-01
Full Text Available We study bundles of Banach algebras ÃÂ€:AÃ¢Â†Â’X, where each fiber Ax=ÃÂ€Ã¢ÂˆÂ’1({x} is a Banach algebra and X is a compact Hausdorff space. In the case where all fibers are commutative, we investigate how the Gelfand representation of the section space algebra ÃŽÂ“(ÃÂ€ relates to the Gelfand representation of the fibers. In the general case, we investigate how adjoining an identity to the bundle ÃÂ€:AÃ¢Â†Â’X relates to the standard adjunction of identities to the fibers.
Banach空间范数的 k-点态粗性和 k-粗性%k- pointwise roughness and k- roughness on Banach spaces
Institute of Scientific and Technical Information of China (English)
义德日胡; 苏雅拉图
2012-01-01
对 Banach 空间范数引入了 k-点态粗和 k-粗的概念，利用 Banach 空间理论的方法，给出了 x ∈ S(X)为范数的 k-粗糙点和 X 的范数是 k-粗的一些充分必要条件，证明了(k +1)-粗糙点是 k-粗糙点以及 k-粗糙点与 Fr´echet 可微性的一些结果。特别地，在 k =1的情形下蕴含了关于范数的粗糙点、点态粗范数和粗范数的相应结果% In this paper, the k- pointwise rough and k- rough norm on Banach space are introduced. By the method of Banach space theory, the some necessary and suﬃcient conditions of k- rough point of norm and k-rough norm of X are given respectively. We proved that (k + 1)- rough point is k- rough point and obtained some results related with k- rough point and Fr´echet differentiability. In particular, when k = 1 our results contains the results of about rough point of norm, pointwise rough norm and rough norm.
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: 1.120, year: 2014 http://www.sciencedirect.com/science/article/pii/S0022247X15006836
One-sided interpolation of injective tensor products of Banach spaces
Michels, Carsten
2007-01-01
The Kouba formula for the complex interpolation of injective tensor products requires all spaces involved to be at least of cotype $2$. We show that this can be weakened when one side of the tensor products is fixed.
CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES
Institute of Scientific and Technical Information of China (English)
HANDEGUANG
1996-01-01
This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that erevy linear derivation of a nest algebra algN is continuous provided that one of the following conditions is satisfied:(1)0+（包含）0.(2)X-（包含于）X.(3)there exists a non-trivial idempotnet p in algN such that the range of p belongs to N, It is also proved that every additive derivation of a nest algebra is automatically linear if the underlying normed space is infinite dimemnsional.
Variational Formulas of Poincaré-Type Inequalities in Banach Spaces of Functions on the Line
Institute of Scientific and Technical Information of China (English)
Mu Fa CHEN
2002-01-01
Motivated from the study on logarithmic Sobolev, Nash and other functional inequalities,spaces of functions on the line. Explicit criteria for the inequalities to hold and explicit estimatesfor the optimal constants in the inequalities are presented. As a typical application, the logarithmicSobolev constant is carefully examined.
New Fixed Point Results with PPF Dependence in Banach Spaces Endowed with a Graph
Hussain, N.; S. Khaleghizadeh; P. Salimi; Akbar, F.
2013-01-01
We introduce the concept of an ${\\alpha }_{c}$ -admissible non-self-mappings with respect to ${\\eta }_{c}$ and establish the existence of PPF dependent fixed and coincidence point theorems for ${\\alpha }_{c}{\\eta }_{c}$ - $\\psi $ -contractive non-self-mappings in the Razumikhin class. As applications of our PPF dependent fixed point and coincidence point theorems, we derive some new fixed and coincidence point results for $\\psi $ -contractions whenever the range space is endowed with a graph ...
Botelho, Fabio
2014-01-01
This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.
$\\sigma $ -Approximately Contractible Banach Algebras
Momeni, M; Yazdanpanah, T.; Mardanbeigi, M. R.
2012-01-01
We investigate $\\sigma $ -approximate contractibility and $\\sigma $ -approximate amenability of Banach algebras, which are extensions of usual notions of contractibility and amenability, respectively, where $\\sigma $ is a dense range or an idempotent bounded endomorphism of the corresponding Banach algebra.
Institute of Scientific and Technical Information of China (English)
娄健; 何欣枫; 何震
2009-01-01
In this paper,we introduce and study a new system of variational inclusions involving (H,η)-monotone operators in Banach space.Using the resolvent operator associated with (H,η)-monotone operators,we prove the existence and uniqueness of solutions for this new system of variational inclusions.We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the iterative sequence generated by the algorithm.
Fréchet differential of a power series in Banach algebras
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Benedetto Silvestri
2010-01-01
Full Text Available We present two new forms in which the Fréchet differential of a power series in a unitary Banach algebra can be expressed in terms of absolutely convergent series involving the commutant \\(C(T : A \\mapsto [A,T]\\. Then we apply the results to study series of vector-valued functions on domains in Banach spaces and to the analytic functional calculus in a complex Banach space.
An inner product for a Banach-algebra
International Nuclear Information System (INIS)
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
A Generation Condition of Integrated Bisemigroup on Banach Space%Banach空间积分双半群的生成条件
Institute of Scientific and Technical Information of China (English)
许跟起; 邵琛
2002-01-01
研究Banach空间中积分双半群的生成条件. 利用算子A的豫解算子,给出了积分双半群T(t)的生成定理. 结果表明:如果对任意的x∈X,f∈X*,以及()|λ|≤δ,λ∈ρ(A),有∈Lp(R),则存在算子族S(t), t∈R,S(t)强连续且满足积分双半群的定义.%The generation condition of integrated bisemigroup in Banach space is studied in this paper. Using the resolvent of operator A, a generation theorem of integrated bisemigroup T(t) is proved. The result is showed that if ()|λ|≤δ,λ∈ρ(A), and satisfy 〈∈Lp(R), for all x∈X, f∈X*, then there exists a family operators S(t), t∈R, which is strongly continuous and satisfies the definition of integrated bisemigroup.
Banach Algebras Associated to Lax Pairs
Glazebrook, James F.
2015-04-01
Lax pairs featuring in the theory of integrable systems are known to be constructed from a commutative algebra of formal pseudodifferential operators known as the Burchnall- Chaundy algebra. Such pairs induce the well known KP flows on a restricted infinite-dimensional Grassmannian. The latter can be exhibited as a Banach homogeneous space constructed from a Banach *-algebra. It is shown that this commutative algebra of operators generating Lax pairs can be associated with a commutative C*-subalgebra in the C*-norm completion of the *-algebra. In relationship to the Bose-Fermi correspondence and the theory of vertex operators, this C*-algebra has an association with the CAR algebra of operators as represented on Fermionic Fock space by the Gelfand-Naimark-Segal construction. Instrumental is the Plücker embedding of the restricted Grassmannian into the projective space of the associated Hilbert space. The related Baker and tau-functions provide a connection between these two C*-algebras, following which their respective state spaces and Jordan-Lie-Banach algebras structures can be compared.
Spectral synthesis for Banach Algebras II
Feinstein, J. F.; Somerset, D. W. B.
1999-01-01
This paper continues the study of spectral synthesis and the topologies $\\tau_{\\infty}$ and $\\tau_r$ on the ideal space of a Banach algebra, concentrating particularly on the class of Haagerup tensor products of C$^*$-algebras. For this class, it is shown that spectral synthesis is equivalent to the Hausdorffness of $\\tau_{\\infty}$. Under a weak extra condition, spectral synthesis is shown to be equivalent to the Hausdorffness of $\\tau_r$.
Fundamental aspects of vector-valued Banach limits
Garcia-Pacheco, F. J.; Perez-Fernandez, F. J.
2016-04-01
This paper is divided into four parts. In the first we study the existence of vector-valued Banach limits and show that a real Banach space with a monotone Schauder basis admits vector-valued Banach limits if and only if it is 1-complemented in its bidual. In the second we prove two vector-valued versions of Lorentz' intrinsic characterization of almost convergence. In the third we show that the unit sphere in the space of all continuous linear operators from \\ell_∞(X) to X which are invariant under the shift operator on \\ell_∞(X) cannot be obtained via compositions of surjective linear isometries with vector-valued Banach limits. In the final part we show that if X enjoys the Krein-Milman property, then the set of vector-valued Banach limits is a face of the unit ball in the space of all continuous linear operators from \\ell_∞(X) to X which are invariant under the shift operator on \\ell_∞(X).
International Nuclear Information System (INIS)
From a special class of systems has been used the linear homogeneous differential equations with impulse effect in Minkowski space field theory with time dependent boundary conditions, i.e. those of moving mirrors. The field theoretical approach for studing the properties of the vacuum starts from an analysis of the behaviour of local field quantities in Minkowski space with uniformly moving mirrors. For the impulsive moving mirror model is the real process of interaction between the quantum field and the external mirror a subject to disturbances in its evolution acting in time very short compared with the entire duration of the process. The stability of the process in the stability of the vacuum state energy. 7 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.
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. fixed pointtheoryandapplications.com/content/2010/1/852346
Derivations into Duals of Ideals of Banach Algebras
Indian Academy of Sciences (India)
M E Gorgi; T Yazdanpanah
2004-11-01
We introduce two notions of amenability for a Banach algebra $\\mathcal{A}$. Let be a closed two-sided ideal in $\\mathcal{A}$, we say $\\mathcal{A}$ is -weakly amenable if the first cohomology group of $\\mathcal{A}$ with coefficients in the dual space * is zero; i.e., $H^1(\\mathcal{A},I^*) =\\{0\\}$, and, $\\mathcal{A}$ is ideally amenable if $\\mathcal{A}$ is -weakly amenable for every closed two-sided ideal in $\\mathcal{A}$. We relate these concepts to weak amenability of Banach algebras. We also show that ideal amenability is different from amenability and weak amenability. We study the -weak amenability of a Banach algebra $\\mathcal{A}$ for some special closed two-sided ideal .
Institute of Scientific and Technical Information of China (English)
张育梅; 程毅; 王靖华
2012-01-01
利用同伦方法证明了一类发展方程反周期解在Banach空间中的存在性和唯一性.先构造同伦方程,再对方程做先验估计.最后通过定义解算子,运用拓扑度方法,给出了发展方程反周期解存在的充分条件.%We proved the existence and uniqueness of a class of evolution equation in Banach space using homotopy methods. We constructed a homotopy equation and made α priori, estimate to this equation. Under the definition solution operator conditions, a sufficient condition of existence of solutions was obtained by means of topological degree method.
Institute of Scientific and Technical Information of China (English)
赵吕慧子; 孙经先
2011-01-01
The definition of a class of new operators, convex-power 1-set-contraction operators in Banach spaces is giv en , and the existence of fixed points of this class of operators is studied. By using methods of approximation by opera tors, the fixed point theorems of Rothe and Altman type convex-power 1-set-contraction operators is obtained, which generalize fixed point theorems of 1-set-contraction operators.%在Banach空间中给出了一类新算子——凸幂1集压缩算子的定义,研究了这类新算子不动点的存在性问题,利用算子逼近的方法,获得了Rothe及Altman型凸幂1集压缩算子的不动点定理,推广了1集压缩算子的不动点定理.
Stability of functional equations in Banach algebras
Cho, Yeol Je; Rassias, Themistocles M; Saadati, Reza
2015-01-01
Some of the most recent and significant results on homomorphisms and derivations in Banach algebras, quasi-Banach algebras, C*-algebras, C*-ternary algebras, non-Archimedean Banach algebras and multi-normed algebras are presented in this book. A brief introduction for functional equations and their stability is provided with historical remarks. Since the homomorphisms and derivations in Banach algebras are additive and R-linear or C-linear, the stability problems for additive functional equations and additive mappings are studied in detail. The latest results are discussed and examined in stability theory for new functional equations and functional inequalities in Banach algebras and C*-algebras, non-Archimedean Banach algebras, non-Archimedean C*-algebras, multi-Banach algebras and multi-C*-algebras. Graduate students with an understanding of operator theory, functional analysis, functional equations and analytic inequalities will find this book useful for furthering their understanding and discovering the l...
Institute of Scientific and Technical Information of China (English)
Abbas NAJATI
2009-01-01
In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi-Banach algebras associated with the following Pexiderized Jensen functional equation f(x+y/2+z)-g(x-y/2+z)=h(y).This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soe., 72, 297-300 (1978).
Several complex variables and Banach algebras
International Nuclear Information System (INIS)
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)
Approximately -Jordan Homomorphisms on Banach Algebras
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Karimi T
2009-01-01
Full Text Available Let , and let be two rings. An additive map is called -Jordan homomorphism if for all . In this paper, we establish the Hyers-Ulam-Rassias stability of -Jordan homomorphisms on Banach algebras. Also we show that (a to each approximate 3-Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique 3-ring homomorphism near to , (b to each approximate -Jordan homomorphism between two commutative Banach algebras there corresponds a unique -ring homomorphism near to for all .
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: 0.787, year: 2014 http://link.springer.com/article/10.1007%2Fs11856-015-1155-y
Segal algebras in commutative Banach algebras
INOUE, Jyunji; TAKAHASI, Sin-Ei
2014-01-01
The notion of Reiter's Segal algebra in commutative group algebras is generalized to a notion of Segal algebra in more general classes of commutative Banach algebras. Then we introduce a family of Segal algebras in commutative Banach algebras under considerations and study some properties of them.
Institute of Scientific and Technical Information of China (English)
刘玉波; 张凤敏; 苟长义
2009-01-01
首先证明了取值于Banach空间上强连续的向量值函数是可积分的;然后用初等方法证明了向量值函数的柯西积分公式和高阶导数公式;最后讨论了取值于lp(p≥1)空间上的向量值函数解析、可积、柯西积分公式和高阶导数公式与其各分量函数的关系和表示形式,并且给出了有限维赋范线性空间上的向量值函数连续、解析、可积、柯西定理、柯西积分公式和高阶导数公式与其各分量函数的关系和表示形式.%The strongly continuous vector valued functions in Banach space are proved integrable. The Cauchy integral for-mula and higher.derivative formula of vector-valued functions are proved using the elementary method. The relationship be-tween vector valued functions in the space of lp (p≥1) and their componential functions about analyticity, integrability, the Cauchy integral formula and higher derivative formula are discussed. And the relationship between vector valued functions in finite dimensional normed linear space and their componential functions about continuity, analyticity, integrability, Cauchys theorem, the Cauchy integral formula and higher derivative formula are also given.
The Banach-Mazur-Schmidt game and the Banach-Mazur-McMullen game
Fishman, Lior; Reams, Vanessa; Simmons, David
2015-01-01
We introduce two new mathematical games, the Banach-Mazur-Schmidt game and the Banach-Mazur-McMullen game, merging well-known games. We investigate the properties of the games, as well as providing an application to Diophantine approximation theory, analyzing the geometric structure of certain Diophantine sets.
An elementary approach to a lattice-valued Banach-Stone Theorem
Jinxi Chen
2007-01-01
Let $ X $ and $ Y $ be compact Hausdorff spaces, and $ E $ be a nonzero real Banach lattice. In this note, we give an elementary proof of a lattice-valued Banach-Stone theorem by Cao, Reilly and Xiong [3] which asserts that if there exists a Riesz isomorphism $ \\Phi: C(X,E)\\rightarrow C(Y,\\mathbb{R}) $ such that $ \\Phi(f) $ has no zeros if $ f $ has none, then $ X $ is homeomorphic to $ Y $ and $ E $ is Riesz isomorphic to $ \\mathbb{R} $.
Banach function algebras and certain polynomially norm-preserving maps
Hosseini, Maliheh; Sady, Fereshteh
2012-01-01
Let $A$ and $B$ be Banach function algebras on compact Hausdorff spaces $X$ and $Y$, respectively. Given a non-zero scalar $\\alpha$and $s,t\\in \\Bbb N$ we characterize the general form of suitable powers of surjective maps $T, T': A \\longrightarrow B$ satisfying $\\|(Tf)^s (T'g)^t-\\alpha\\|_Y=\\|f^s g^t-\\alpha \\|_X$, for all $f,g \\in A$, where $\\|\\cdot \\|_X$ and $\\|\\cdot \\|_Y$ denote the supremum norms on $X$ and $Y$, respectively. A similar result is given for the case where $T...
Eventually and asymptotically positive semigroups on Banach lattices
Daners, Daniel; Glück, Jochen; Kennedy, James B.
2016-09-01
We develop a theory of eventually positive C0-semigroups on Banach lattices, that is, of semigroups for which, for every positive initial value, the solution of the corresponding Cauchy problem becomes positive for large times. We give characterisations of such semigroups by means of spectral and resolvent properties of the corresponding generators, complementing existing results on spaces of continuous functions. This enables us to treat a range of new examples including the square of the Laplacian with Dirichlet boundary conditions, the bi-Laplacian on Lp-spaces, the Dirichlet-to-Neumann operator on L2 and the Laplacian with non-local boundary conditions on L2 within the one unified theory. We also introduce and analyse a weaker notion of eventual positivity which we call "asymptotic positivity", where trajectories associated with positive initial data converge to the positive cone in the Banach lattice as t → ∞. This allows us to discuss further examples which do not fall within the above-mentioned framework, among them a network flow with non-positive mass transition and a certain delay differential equation.
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...
Tensor products of commutative Banach algebras
Directory of Open Access Journals (Sweden)
Shobha Madan
1982-09-01
Full Text Available Let A1, A2 be commutative semisimple Banach algebras and A1Ã¢ÂŠÂ—Ã¢ÂˆÂ‚A2 be their projective tensor product. We prove that, if A1Ã¢ÂŠÂ—Ã¢ÂˆÂ‚A2 is a group algebra (measure algebra of a locally compact abelian group, then so are A1 and A2. As a consequence, we prove that, if G is a locally compact abelian group and A is a comutative semi-simple Banach algebra, then the Banach algebra L1(G,A of A-valued Bochner integrable functions on G is a group algebra if and only if A is a group algebra. Furthermore, if A has the Radon-Nikodym property, then the Banach algebra M(G,A of A-valued regular Borel measures of bounded variation on G is a measure algebra only if A is a measure algebra.
Admissibility of Linear Systems in Banach Spaces
Institute of Scientific and Technical Information of China (English)
GUO Fa-ming
2005-01-01
In this paper, infinite-time p-admissibility of unbounded operators is introduced and the Co-semigroup characterization of the infinite-time p-admissibility of unbounded observation operators is given. Moreover, the analogous result for the infinite-time p-admissibility of unbounded control operators is presented.
(2-1)-Ideal amenability of triangular banach algebras
Indian Academy of Sciences (India)
S Etemad; M Ettefagh
2015-05-01
Let $\\mathcal{A}$ and $\\mathcal{B}$ be two unital Banach algebras and let $\\mathcal{M}$ be an unital Banach $\\mathcal{A}$, $\\mathcal{B}$-module. Also, let $\\mathcal{T}=\\left[\\begin{smallmatrix} \\mathcal{A} & \\mathcal{M}\\\\ & \\mathcal{B}\\end{smallmatrix}\\right]$ be the corresponding triangular Banach algebra. Forrest and Marcoux (Trans. Amer. Math. Soc. 354 (2002) 1435–1452) have studied the -weak amenability of triangular Banach algebras. In this paper, we investigate (2-1)-ideal amenability of $\\mathcal{T}$ for all ≥ 1. We introduce the structure of ideals of these Banach algebras and then, we show that (2-1)-ideal amenability of $\\mathcal{T}$ depends on (2-1)-ideal amenability of Banach algebras $\\mathcal{A}$ and $\\mathcal{B}$.
Multipliers of Weighted Semigroups and Associated Beurling Banach Algebras
Indian Academy of Sciences (India)
S J Bhatt; P A Dabhi; H V Dedania
2011-11-01
Given a weighted discrete abelian semigroup $(S,)$, the semigroup $M_(S)$ of -bounded multipliers as well as the Rees quotient $M_(S)/S$ together with their respective weights $\\overline{}$ and $\\overline{}_q$ induced by are studied; for a large class of weights , the quotient $\\ell^1(M_(S),\\overline{})/\\ell^1(S,)$ is realized as a Beurling algebra on the quotient semigroup $M_(S)/S$; the Gel’fand spaces of these algebras are determined; and Banach algebra properties like semisimplicity, uniqueness of uniform norm and regularity of associated Beurling algebras on these semigroups are investigated. The involutive analogues of these are also considered. The results are exhibited in the context of several examples.
A Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergences
Loaiza Ossa, Gabriel Ignacio; Quiceno Echavarría, Héctor Román
2013-01-01
For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built. In this paper, the geometry induced on this manifold is characterized by q-divergence functionals. This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections. Moreover, the classical Amari’s α-connections appears ...
Sifat Aljabar Banach Komutatif dan Elemen Identitas pada Kelas D(K
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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
Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras
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Hirasawa Go
2005-01-01
Full Text Available We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias stability of a Jordan homomorphism between Banach algebras. As a direct corollary, we show that to each approximate Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique ring homomorphism near to .
A type (4) space in (FR)-classification
Argyros, Spiros A; Pelczar-Barwacz, Anna
2012-01-01
We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal list within the framework of Gowers' classification program of Banach spaces. The space is an unconditional variant of the Gowers Hereditarily Indecomposable space with asymptotically unconditional basis.
On $\\phi$-ergodic property of Banach modules
Nemati, Mehdi
2015-01-01
Let ${\\mathcal A}$ be a Banach algebra and let $\\phi$ be a non-zero character on ${\\mathcal A}$. We introduce the notion of $\\phi$-ergodic property for a Banach right ${\\mathcal A}$-module $X$. This concept considerably generalizes the existence of $\\phi$-means of norm one on ${\\mathcal A}^*$. We also show that the $\\phi$-ergodic property of $X$ is related to some other properties such as a Hahn-Banach type extension property and the existence of $\\phi$-means of norm one on ...
Very Smooth Points of Spaces of Operators
Indian Academy of Sciences (India)
T S S R K Rao
2003-02-01
In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when the space of compact operators is an -ideal in the space of bounded operators, a very smooth operator attains its norm at a unique vector (up to a constant multiple) and ( ) is a very smooth point of the range space. We show that if for every equivalent norm on a Banach space, the dual unit 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.
Ideal Amenability of Banach Algebras on Locally Compact Groups
Indian Academy of Sciences (India)
M Eshaghi Gordji; S A R Hosseiniun
2005-08-01
In this paper we study the ideal amenability of Banach algebras. Let $\\mathcal{A}$ be a Banach algebra and let be a closed two-sided ideal in $\\mathcal{A}, \\mathcal{A}$ is -weakly amenable if $H^1(\\mathcal{A},I^∗)=\\{0\\}$. Further, $\\mathcal{A}$ is ideally amenable if $\\mathcal{A}$ is -weakly amenable for every closed two-sided ideal in $\\mathcal{A}$. We know that a continuous homomorphic image of an amenable Banach algebra is again amenable. We show that for ideal amenability the homomorphism property for suitable direct summands is true similar to weak amenability and we apply this result for ideal amenability of Banach algebras on locally compact groups.
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
Stability of -Jordan Homomorphisms from a Normed Algebra to a Banach Algebra
Directory of Open Access Journals (Sweden)
Yang-Hi Lee
2013-01-01
Full Text Available We establish the hyperstability of -Jordan homomorphisms from a normed algebra to a Banach algebra, and also we show that an -Jordan homomorphism between two commutative Banach algebras is an -ring homomorphism.
Atomic Decompositions of Weak Hardy Spaces of B-Valued Martingales
Institute of Scientific and Technical Information of China (English)
MA Tao; LIU Peide
2006-01-01
The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0 ＜ r≤ 1.Here the results are connected closely with the p-uniform smoothness and q-uniform convexity of Banach spaces which the martingales take values in.
Institute of Scientific and Technical Information of China (English)
2008-01-01
Let (Ω,A,μ) be a probability space, K the scalar field R of real numbers or C of complex numbers,and (S,X) a random normed space over K with base (Ω,A,μ). Denote the support of (S,X) by E, namely E is the essential supremum of the set {A ∈ A : there exists an element p in S such that Xp(ω) > 0 for almost all ω in A}. In this paper, Banach-Alaoglu theorem in a random normed space is first established as follows: The random closed unit ball S*(1) = {f ∈ S* : Xf* 1} of the random conjugate space (S*,X*) of (S,X) is compact under the random weak star topology on (S*,X*) iff E∩A=: {E∩A | A ∈ A} is essentially purely μ-atomic (namely, there exists a disjoint family {An : n ∈ N} of at most countably many μ-atoms from E∩A such that E =∪n∞=1 An and for each element F in E∩A, there is an H in the σ-algebra generated by {An : n ∈ N} satisfying μ(F △H) = 0), whose proof forces us to provide a key topological skill, and thus is much more involved than the corresponding classical case. Further, Banach-Bourbaki-Kakutani-mulian (briefly, BBKS) theorem in a complete random normed module is established as follows: If (S,X) is a complete random normed module, then the random closed unit ball S(1) = {p ∈ S : Xp 1} of (S,X) is compact under the random weak topology on (S,X) iff both (S,X) is random reflexive and E∩A is essentially purely μ-atomic. Our recent work shows that the famous classical James theorem still holds for an arbitrary complete random normed module, namely a complete random normed module is random reflexive iff the random norm of an arbitrary almost surely bounded random linear functional on it is attainable on its random closed unit ball, but this paper shows that the classical Banach-Alaoglu theorem and BBKS theorem do not hold universally for complete random normed modules unless they possess extremely simple stratification structure, namely their supports are essentially purely μ-atomic. Combining the James theorem and
Institute of Scientific and Technical Information of China (English)
GUO TieXin
2008-01-01
Let(Ω,A,μ)be a probability space,K the scalar field R of real numbers or C of complex numbers,and(S,X)a random normed space over K with base(Ω,A,μ).Denote the support of(S,X)by E,namely E is the essentiaI supremum of the ser {A∈A:there exists an element p in S such that Xp(ω)＞0 for almost all ω in A}. In this paper,Banach-Alaoglu theorem in a random normed space is first established as follows:The random closed unit ball S*(1)={f∈S*:X*f≤1}of the random conjugate space(S*,x*)of(S,X)is compact under the random weak star topology on (S*,X*)iff E∩A=:{E∩A|A∈A}is essentially purely μ-atomic(namely,there exists a disjoint family{An:n∈N}of at most countably many μ-atoms from E∩A such that E=∪∞n=1 An and for each element F in E∩A,there is an H in the σ-algebra generated by{An:n∈N)satisfying μ(F△H)=0),whose proof forces us to provide a key topological skill,and thus is much more involved than the corresponding classical case.Further,Banach-Bourbaki-Kakutani-Smulian(briefly,BBKS)theorem in a complete random normed module is established as follows:If(S,X)is a complete random normed module,then the random closed unit ball S(1)={p∈S:Xp≤1}of(S,X)is compact under the random weak topology on(S,X)iff both(S,X)is random reflexive and E∩A is essentially purely μ-atomic.Our recent work shows that the famous classical James theorem still holds for an arbitrary complete random normed module,namely a complete random normed module is random reflexive iff the random norm of an arbitrary almost surely bounded random linear functional on it is attainable on its random closed unit ball,but this paper shows that the classical Banach-Alaoglu theorem and BBKS theorem do not hold universally for complete random normed modules unless they possess extremely simple stratification structure,namely their supports are essentially purely μ-atomic.Combining the James theorem and BBKS theorem in complete random normed modules leads directly to an interesting
The Classical Integral Operators in Weighted Lorentz Spaces with Variable Exponent.
D.M. Israfilov; N.P. Tuzkaya
2006-01-01
In this paper the Lorentz spaces with variable exponent are introduced. These Banach function spaces are defined on the base of variable Lebesgue spaces. Boundedness of classical integral operators are proved in variable Lorentz spaces.
Approximately Linear Mappings in Banach Modules over a C*-algebra
Institute of Scientific and Technical Information of China (English)
Choonkil PARK; Jian Lian CUI
2007-01-01
Let X and Y be vector spaces. The authors show that a mapping f: X → Y satisfies the functional equation 2df(∑2dj=1(-1)j+1xj/2d)=∑2dj=1(-1)j+1f(xj) with f(0) = 0 if and only if the mapping f: X → Y is Cauchy additive, and prove the stability of the functional equation (++) in Banach modules over a unital C*-algebra, and in Poisson Banach modules over a unital Poisson C*-algebra. Let A and B be unital C*-algebras, Poisson C*-algebras or Poisson JC*-algebras. As an application, the authors show that every almost homomorphism h: A → B of A into B is a homomorphism when h((2d-1)nuy) = h((2d-1)nu)h(y) or h((2d-1)nuoy) = h((2d-1)nu)oh(y) for all unitaries u ∈ A, all y ∈ A, n= 0, 1, 2,....Moreover, the authors prove the stability of homomorphisms in C*-algebras, Poisson C*-algebras or Poisson JC*-algebras.
The smooth Banach submanifold B*(E,F) in B(E,F)
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Let E,F be two Banach spaces,B(E,F),B+(E,F),Φ(E,F),SΦ(E,F) and R(E,F) be bounded linear,double splitting,Fredholm,semi-Frdholm and finite rank operators from E into F,respectively. Let Σ be any one of the following sets:{T ∈Φ(E,F):Index T=constant and dim N(T)=constant},{T ∈ SΦ(E,F):either dim N(T)=constant< ∞ or codim R(T)=constant< ∞} and {T ∈ R(E,F):Rank T=constant< ∞}. Then it is known that Σ is a smooth submanifold of B(E,F) with the tangent space TAΣ={B ∈ B(E,F):BN(A)-R(A) } for any A ∈Σ. However,for B*(E,F)={T ∈ B+(E,F):dimN(T)=codimR(T)= ∞} without the characteristic numbers,dimN(A) ,codimR(A) ,index(A) and Rank(A) of the equivalent classes above,it is very diffcult to find which class of operators in B*(E,E) forms a smooth submanifold of B(E,F) . Fortunately,we find that B*(E,F) is just a smooth submanifold of B(E,F) with the tangent space TAB*(E,F)={T ∈ B(E,F) :T N(A) -R(A) } for each A ∈ B*(E,F) . Thus the geometric construction of B+(E,F) is obtained,i.e.,B+(E,F) is a smooth Banach submanifold of B(E,F) ,which is the union of the previous smooth submanifolds disjoint from each other. Meanwhile we give a smooth submanifold S(A) of B(E,F) ,modeled on a fixed Banach space and containing A for any A ∈ B+(E,F) . To end these,results on the generalized inverse perturbation analysis are generalized. Specially,in the case E=F=Rn,it is obtained that the set Σr of all n × n matrices A with Rank(A)=r < n is an arcwise connected and smooth hypersurface(submanifold) in B(Rn) with dimΣr=2nr-r2. Then a new geometrical construction of B(Rn) ,analogous to B+(E,F) ,is given besides its analysis and algebra constructions known well.
The Socle and Finite Dimensionality of some Banach Algebras
Indian Academy of Sciences (India)
Ali Ghaffari; Ali Reza Medghalchi
2005-08-01
The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional. One of the main results in Theorem 2 which states that for a locally compact group , is compact if there exists a measure in $\\mathrm{Soc} (L^1(G))$ such that () ≠ 0. We also prove that is finite if $\\mathrm{Soc}(M(G))$ is closed and every nonzero left ideal in () contains a minimal left ideal.
de Jeu, Marcel
2012-01-01
If X is a compact Hausdorff space, supplied with a homeomorphism, then a crossed product involutive Banach algebra is naturally associated with these data. If X consists of one point, then this algebra is the group algebra of the integers. In this paper, we study spectral synthesis for the closed ideals of this associated algebra in two versions, one modeled after C(X), and one modeled after the group algebra of the integers. We identify the closed ideals which are equal to (what is the analogue of) the kernel of their hull, and determine when this holds for all closed ideals, i.e., when spectral synthesis holds. In both models, this is the case precisely when the homeomorphism has no periodic points.
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.
SMOOTH AND PATH CONNECTED BANACH SUBMANIFOLD ∑r OF B(E,F) AND A DIMENSION FORMULA IN B(IRn,IRm)
Institute of Scientific and Technical Information of China (English)
Jipu Ma
2008-01-01
Given two Banach spaces E, F, let B(E, F) be the set of all bounded linear oper-ators from E into F, ∑r the set of all operators of finite rank r in B(E, F), and ∑#r the number of path connected components of ∑r. It is known that ∑r is a smooth Banach submani-fold in B(E, F) with given expression of its tangent space at each A ∈∑r. In this paper, the equality ∑#r = 1 is proved. Consequently, the following theorem is obtained: for any non-negative integer r, ∑r is a smooth and path connected Banach submanifold in B(E, F) with the tangent space TA∑r={B∈B(E,F): BN(A) R(A)} at each A∈∑r if dim F = ∞. Note that the routine method can hardly be applied here. So in addition to the nice topological and geometric property of ∑r the method presented in this paper is also interesting. As an application of this result, it is proved that if E = IRn and F = IRm, then ∑r is a smooth and path connected submanifold of B(IRn,IRm) and its dimension is dim ∑r = (m + n)r- r2 for each r, 0 ≤ r < min{n,m}.
Regular norm and the operator semi-norm on a non-unital Banach Algebra
Orenstein, Adam
2014-01-01
We show that if $\\mathfrak{A}$ is a commutative complex non-unital Banach Algebra with norm $\\|\\cdot\\|$, then $\\|\\cdot\\|$ is regular on $\\mathfrak{A}$ if and only if $\\|\\cdot\\|_{op}$ is a norm on $\\mathfrak{A}\\oplus \\mathbb{C}$ and $\\mathfrak{A}\\oplus\\mathbb{C}$ is a commutative complex Banach Algebra with respect to $\\|\\cdot\\|_{op}$.
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.
Convexity and w*-compactness in Banach spaces
Czech Academy of Sciences Publication Activity Database
Granero, A. S.; Hájek, Petr Pavel; Santalucía, V. M.
2004-01-01
Roč. 328, č. 4 (2004), s. 625-631. ISSN 0025-5831 R&D Projects: GA ČR GA201/01/1198; GA AV ČR IAA1019205 Institutional research plan: CEZ:AV0Z1019905 Keywords : krein theorem * weak compactness Subject RIV: BA - General Mathematics Impact factor: 0.790, year: 2004
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.
Existence theorems for functional differential equations in Banach spaces
Sghir, A
2009-01-01
This paper concernes with the study of existence theorems for a general class of functional differential equations of the form u'(t)=f(t,u circ g(t,cdot)).The obtained results generalize the retarded functional differential equations [5], [6], [8] and cover singular functional differential equations [1], [3], [4], [7], [9], [12].
On the topological classification of starlike bodies in Banach spaces
Azagra Rueda, Daniel; Dobrowolski, Tadeusz
2003-01-01
Starlike bodies are interesting in nonlinear analysis because they are strongly related to polynomials and smooth bump functions, and their topological and geometrical properties are therefore worth studying. In this note we consider the question as to what extent the known results on topological classification of convex bodies can be generalized for the class of starlike bodies, and we obtain two main results in this line, one which follows the traditional Bessaga-Klee scheme for the classif...
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
The compactum of a semi-simple commutative Banach algebra
Directory of Open Access Journals (Sweden)
Abduliah H. Al-Moajil
1984-12-01
Full Text Available Let A be a commutative semi-simple Banach algebra such that the set consisting of finite sums of elements from minimal left ideals coincides with that of finite sums of elements from minimal right ideals. Let S(A (the socle of A denote this set. Let C(A denote the set of elements x in A such that the map aÃ¢Â†Â’xax is compact. It is shown that C(A is the norm closure of S(A.
Simplified and Equivalent Characterizations of Banach Limit Functional and Strong Almost Convergence
You, Chao
2009-01-01
In this paper, we give simplified and equivalent characterizations of Banach limit functional, which is the minimum requirement to characterize strong almost convergence. With this machinery, we show that Hajdukovic's quasi-almost convergence is equivalent to strong almost convergence.
Convolution and Involution on Function Spaces of Homogeneous Spaces
Farashahi, Arash Ghaani
2012-01-01
Let $G$ be a locally compact group and also let $H$ be a compact subgroup of $G$. It is shown that, if $\\mu$ is a relatively invariant measure on $G/H$ then there is a well-defined convolution on $L^1(G/H,\\mu)$ such that the Banach space $L^1(G/H,\\mu)$ becomes a Banach algebra. We also find a generalized definition of this convolution for other $L^p$-spaces. Finally, we show that various types of involutions can be considered on $G/H$.
Vela Velupillai, K.
2014-01-01
The Hahn-Banach Theorem plays a crucial role in the second fundamental theorem of welfare economics. To date, all mathematical economics and advanced general equilibrium textbooks concentrate on using nonconstructive or incomputable versions of this celebrated theorem. In this paper we argue for the introduction of constructive or computable Hahn-Banach theorems in mathematical economics and advanced general equilibrium theory. The suggested modification would make applied and policy-oriented...
Approximately
Karimi T; Kaboli Gharetapeh S; Gordji MEshaghi
2009-01-01
Let , and let be two rings. An additive map is called -Jordan homomorphism if for all . In this paper, we establish the Hyers-Ulam-Rassias stability of -Jordan homomorphisms on Banach algebras. Also we show that (a) to each approximate 3-Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique 3-ring homomorphism near to , (b) to each approximate -Jordan homomorphism between two commutative Banach algebras there corresp...
Remark on Regularity of Continuous Operators on AL-Spaces
Institute of Scientific and Technical Information of China (English)
冯勋省; 陈滋利
2004-01-01
Let E and F be Banach lattices. It is known that if every continuous linear operator from E into F is regular, then, under some mild assumptions on E or F, either E is lattice isomorphic to an AL-space or F is lattice isomorphic to an AM-space. Here we present a characterization on an AL-space E such that every bounded linear operator from E into a Banach lattice is regular. A counterexample is also provided, which shows that the results are unexpected even if the domain is an AL-space or the range space is an AM-space.
Reducibility of invertible tuples to the principal component in commutative Banach algebras
Mortini, Raymond; Rupp, Rudolf
2015-10-01
Let A be a complex, commutative unital Banach algebra. We introduce two notions of exponential reducibility of Banach algebra tuples and present an analogue to the Corach-Suárez result on the connection between reducibility in A and in C(M(A)). Our methods are of an analytical nature. Necessary and sufficient geometric/topological conditions are given for reducibility (respectively reducibility to the principal component of Un(A)) whenever the spectrum of A is homeomorphic to a subset of {C}n.
Functional calculus and *-regularity of a class of Banach algebras II
Leung, Chi-Wai; Ng, Chi-Keung
2006-10-01
In this article, we define a natural Banach *-algebra for a C*-dynamical system (A,G,[alpha]) which is slightly bigger than L1(G;A) (they are the same if A is finite-dimensional). We will show that this algebra is *-regular if G has polynomial growth. The main result in this article extends the two main results in [C.W. Leung, C.K. Ng, Functional calculus and *-regularity of a class of Banach algebras, Proc. Amer. Math. Soc., in press].
Stability of a Bi-Additive Functional Equation in Banach Modules Over a C⋆-Algebra
Directory of Open Access Journals (Sweden)
Won-Gil Park
2012-01-01
Full Text Available We solve the bi-additive functional equation f(x+y,z−w+f(x−y,z+w=2f(x,z−2f(y,w and prove that every bi-additive Borel function is bilinear. And we investigate the stability of a bi-additive functional equation in Banach modules over a unital C⋆-algebra.
On solvability of some quadratic functional-integral equation in Banach algebra
International Nuclear Information System (INIS)
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)
Common fixed points for Banach operator pairs from the set of best approximations
Ćirić, L.; Hussain, N.; F. Akbar; Ume, J. S.
2009-01-01
The existence of common fixed point results for a Banach operator pair under certain generalized $\\varphi$-contractions is established. As applications, the corresponding invariant best approximation results are proved. Our results unify and generalize various known results to the more general class of noncommuting mappings.
Central limit theorem for the Banach-valued weakly dependent random variables
International Nuclear Information System (INIS)
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
The Intuitionistic Fuzzy Normed Space of Coefficients
Bilalov, B. T.; S. M. Farahani; Guliyeva, F. A.
2012-01-01
Intuitionistic fuzzy normed space is defined using concepts of $t$ -norm and $t$ -conorm. The concepts of fuzzy completeness, fuzzy minimality, fuzzy biorthogonality, fuzzy basicity, and fuzzy space of coefficients are introduced. Strong completeness of fuzzy space of coefficients with regard to fuzzy norm and strong basicity of canonical system in this space are proved. Strong basicity criterion in fuzzy Banach space is presented in terms of coefficient operator.
Survey on nonlocal games and operator space theory
International Nuclear Information System (INIS)
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
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.
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.
Nonlinear potentials in function spaces
Rao, Murali; Vondraček, Zoran
2002-01-01
We introduce a framework for a nonlinear potential theory without a kernel on a reflexive, strictly convex and smooth Banach space of functions. Nonlinear potentials are defined as images of nonnegative continuous linear functionals on that space under the duality mapping. We study potentials and reduced functions by using a variant of the Gauss-Frostman quadratic functional. The framework allows a development of other main concepts of nonlinear potential theory such as capa...
On Fixed-point theorems in Intuitionistic Fuzzy metric Space
Samanta, T K; Jebril, Iqbal H
2010-01-01
In this paper, first we have established two sets of sufficient conditions for a mapping to have unique fixed point in a intuitionistic fuzzy metric space and then we have redefined the contraction mapping in a intuitionistic fuzzy metric space and thereafter we proved the Banach Fixed Point theorem.
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...
A note on mutiplication operators on Köthe-Bochner spaces
S. S. Khurana
2012-01-01
Let (Ω, A, μ) is a finite measure space, E an order continuous Banach function space over μ, X a Banach space and E(X) the Köthe-Bochner space. A new simple proof is given of the result that a continuous linear operator T: E(X) ® E(X) is a multiplication operator (by a function in L¥) iff T(g x) =g x for everyg Î L¥, f Î E(X), x Î X, x* Î X*.
Bessel and Grüss Type Inequalities in Inner Product Modules over Banach -Algebras
Directory of Open Access Journals (Sweden)
Dragomir SS
2011-01-01
Full Text Available We give an analogue of the Bessel inequality and we state a simple formulation of the Grüss type inequality in inner product -modules, which is a refinement of it. We obtain some further generalization of the Grüss type inequalities in inner product modules over proper -algebras and unital Banach -algebras for -seminorms and positive linear functionals.
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).
The isometric extension of “into” mappings on unit spheres of AL-spaces
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper, we show that if V0 is an isometric mapping from the unit sphere of an AL-space onto the unit sphere of a Banach space E, then V0 can be extended to a linear isometry defined on the whole space.
Garbulińska, Joanna
2011-01-01
We present selected known results and some of their improvements, involving Gurarii spaces. A Banach space is Gurarii if it has certain natural extension property for almost isometric embeddings of finite-dimensional spaces. Deleting the word "almost", we get the notion of a strong Gurarii space. There exists a unique (up to isometry) separable Gurarii space, however strong Gurarii spaces cannot be separable. The structure of the class of non-separable Gurarii spaces seems to be not very well understood. We discuss some of their properties and state some open questions. In particular, we characterize non-separable Gurarii spaces in terms of skeletons of separable subspaces, we construct a non-separable Gurarii space with a projectional resolution of the identity and we show that no strong Gurarii space can be weakly Lindel\\"of determined.
On prime and semiprime rings with generalized derivations and non-commutative Banach algebras
Indian Academy of Sciences (India)
MOHD ARIF RAZA; NADEEM UR REHMAN
2016-08-01
Let $R$ be a prime ring of characteristic different from 2 and $m$ a fixed positive integer. If $R$ admits a generalized derivation associated with a nonzero deviation $d$ such that $[F(x), d(y)]_m = [x, y]$ for all $x$, $y$ in some appropriate subset of $R$, then $R$ is commutative. Moreover, we also examine the case $R$ is a semiprime ring. Finally, we apply the above result to Banach algebras, and we obtain a non-commutative version of the Singer--Werner theorem.
Directory of Open Access Journals (Sweden)
Lakshmi Narayan Mishra
2016-04-01
Full Text Available In the present manuscript, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contains various integral and functional equations that considered in nonlinear analysis and its applications. By utilizing the techniques of noncompactness measures, we operate the fixed point theorems such as Darbo's theorem in Banach algebra concerning the estimate on the solutions. The results obtained in this paper extend and improve essentially some known results in the recent literature. We also provide an example of nonlinear functional-integral equation to show the ability of our main result.
THE FUNCTIONAL DIMENSION OF SOME CLASSES OF SPACES
Institute of Scientific and Technical Information of China (English)
LIU SHANGPING; LI BINGREN
2005-01-01
The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3)Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*, B). Then the functional dimension of (B*, σ(B*, B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.
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 space s * K-monotone symmetric Banach space s * strict monotonicity * lower local uniform monotonicity Subject RIV: BA - General Mathematics Impact factor: 0.918, year: 2014 http://link.springer.com/article/10.1007%2Fs00010-015-0379-6
Topological centers of module actions and cohomological groups of Banach Algebras
Azar, Kazem Azem Haghnejad
2010-01-01
In this paper, first we study some Arens regularity properties of module actions. Let $B$ be a Banach $A-bimodule$ and let ${Z}^\\ell_{B^{**}}(A^{**})$ and ${Z}^\\ell_{A^{**}}(B^{**})$ be the topological centers of the left module action $\\pi_\\ell:~A\\times B\\rightarrow B$ and the right module action $\\pi_r:~B\\times A\\rightarrow B$, respectively. We investigate some relationships between topological center of $A^{**}$, ${Z}_1({A^{**}})$ with respect to the first Arens product and topological centers of module actions ${Z}^\\ell_{B^{**}}(A^{**})$ and ${Z}^\\ell_{A^{**}}(B^{**})$. On the other hand, if $A$ has Mazure property and $B^{**}$ has the left $A^{**}-factorization$, then $Z^\\ell_{A^{**}}(B^{**})=B$, and so for a locally compact non-compact group $G$ with compact covering number $card(G)$, we have $Z^\\ell_{M(G)^{**}}{(L^1(G)^{**})}= {L^1(G)}$ and $Z^\\ell_{L^1(G)^{**}}{(M(G)^{**})}= {M(G)}$. By using the Arens regularity of module actions, we study some cohomological groups properties of Banach algebra and we...
International Nuclear Information System (INIS)
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
Star product realizations of kappa-Minkowski space
Durhuus, Bergfinnur; Sitarz, Andrzej
2011-01-01
We define a family of star products and involutions associated with $\\kappa$-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 $\\kappa$-Minkowski space. Furthermore, we ...
Isometric Reflection Vectors and Characterizations of Hilbert Spaces
Directory of Open Access Journals (Sweden)
Donghai Ji
2014-01-01
Full Text Available A known characterization of Hilbert spaces via isometric reflection vectors is based on the following implication: if the set of isometric reflection vectors in the unit sphere SX of a Banach space X has nonempty interior in SX, then X is a Hilbert space. Applying a recent result based on well-known theorem of Kronecker from number theory, we improve this by substantial reduction of the set of isometric reflection vectors needed in the hypothesis.
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. .
Dinda, Bivas; Jebril, Iqbal H
2011-01-01
In this paper intuitionistic fuzzy {\\psi}-{\\phi}-contractive mappings are introduced. Intuitionistic fuzzy Banach contraction theorem for M-complete non-Archimedean intuitionistic fuzzy metric spaces and intuitionistic fuzzy Elelstein contraction theorem for non-Archimedean intuitionistic fuzzy metric spaces by intuitionistic fuzzy {\\psi}-{\\phi}-contractive mappings are proved.
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.
An Existence Result for Nonlinear Fractional Differential Equations on Banach Spaces
Directory of Open Access Journals (Sweden)
Cabada Alberto
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.
The fixed point theorems of 1-set-contractive operators in Banach space
Directory of Open Access Journals (Sweden)
Wang Shuang
2011-01-01
Full Text Available Abstract In this paper, we obtain some new fixed point theorems and existence theorems of solutions for the equation Ax = μx using properties of strictly convex (concave function and theories of topological degree. Our results and methods are different from the corresponding ones announced by many others. MSC: 47H09, 47H10
Directory of Open Access Journals (Sweden)
Chang Shih-sen
2008-01-01
Full Text Available Abstract In this paper, a new implicit iteration process with errors for finite families of strictly asymptotically pseudocontractive mappings and nonexpansive mappings is introduced. By using the iterative process, some strong convergence theorems to approximating a common fixed point of strictly asymptotically pseudocontractive mappings and nonexpansive mappings are proved. The results presented in the paper are new which extend and improve some recent results of Osilike et al. (2007, Liu (1996, Osilike (2004, Su and Li (2006, Gu (2007, Xu and Ori (2001.
Mouffak Benchohra; Fatima-Zohra Mostefai
2012-01-01
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.
Indian Academy of Sciences (India)
K Balachandran; K Uchiyama
2000-05-01
In this paper we prove the existence of mild and strong solutions of a nonlinear integrodifferential equation of Sobolev type with nonlocal condition. The results are obtained by using semigroup theory and the Schauder fixed point theorem.
Directory of Open Access Journals (Sweden)
Zhiqun Xue
2008-03-01
Full Text Available The purpose of this paper is to compare convergence speed of the Picard and Mann iterations on one hand, Krasnoselskij and Ishikawa iterations on the other hand, for the class of Zamfirescu operators. The results improve corresponding results of (Berinde 2004 and (Babu and Vara Prasad 2006.
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.
k-接近一致光滑Bananch空间%k-Nearly Uniformly Smooth Banach Spaces
Institute of Scientific and Technical Information of China (English)
王翠玲; 魏文展; 周玲丽
2006-01-01
定义k-接近一致光滑模,利用其给出k-接近一致光滑(k-NUS)空间的概念,证明k-接近一致光滑空间与k-接近一致凸空间是对偶概念,同时引入具有w*k性质的空间,给出k-接近一致光滑空间的一个特征刻画,并讨论(k+1)-接近一致光滑空间与接近一致光滑和k-一致光滑(kUS)空间的关系.
NEW FIXED POINT THEOREMS FOR P1-COMPACT MAPPINGS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
F.E. Browder and W. V. Petryshyn[1] defined the topological degree for Aproper mappings and then W. V. Petryshyn[2] studied a class of A-proper mappings, namely,P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn[2], we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder's theorem, Rothe's theorem, Altman's theorem,Petryshyn's theorem, etc.
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes.
Institute of Scientific and Technical Information of China (English)
LIU WeiDong; FU KeAng; ZHANG LiXin
2008-01-01
In this paper, we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables. As an interesting application, we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes.
CONCEPTS OF DICHOTOMY FOR SKEW-EVOLUTION SEMIFLOWS IN BANACH SPACES
Directory of Open Access Journals (Sweden)
Mihail Megan
2011-01-01
Full Text Available In this paper we investigate some dichotomy concepts for skew-evolution semiflows in Banachspaces.Our main objective is to estab-lish relations between these concepts.We motivate our approach byillustrative examples.
On H–Dichotomy for Skew-Evolution Semiflows in Banach Spaces
Directory of Open Access Journals (Sweden)
Stoica Codruţa
2012-04-01
Full Text Available The aim of this paper is to define and characterize a particular case of dichotomy for skew-evolution semiflows, called the H–dichotomy, as a useful tool in describing the behaviors for the solutions of evolution equations that describe phenomena from engineering or economics. The paper emphasizes also other asymptotic properties, as ω–growth and ω–decay, H–stability and H–instability, as well as the classic concept of exponential dichotomy.
ITERATIVE SOLUTIONS FOR SYSTEMS OF NONLINEAR OPERATOR EQUATIONS IN BANACH SPACE
Institute of Scientific and Technical Information of China (English)
宋光兴
2003-01-01
By using partial order method, the existence, uniqueness and iterative ap-proximation of solutions for a class of systems of nonlinear operator equations in Banachspace are discussed. The results obtained in this paper extend and improve recent results.
On the mild solutions of higher-order differential equations in Banach spaces
Directory of Open Access Journals (Sweden)
Nguyen Thanh Lan
2003-01-01
Full Text Available For the higher-order abstract differential equation u(n(t=Au(t+f(t, t∈ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace ℳ of BUC(ℝ,E with respect to the above-mentioned equation in terms of solvability of the operator equation AX−Xn=C. As applications, periodicity and almost periodicity of mild solutions are also proved.
Ferro, Leonardo
2013-01-01
El objetivo principal de esta disertación es el estudio de la teoría de las álgebras de Lie–Jordan Banach y su papel en el marco de la mecánica clásica y cuántica y sus aplicaciones en diferentes ámbitos de las matemáticas. La investigación algebraica de los fundamentos de la física surgió de la búsqueda de una formulación “excepcional” para la mecánica cuántica, que finalmente culminó en la formulación de las álgebras de Jordan y las posteriores C∗–álgebras.............
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
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.
Functional calculus on real interpolation spaces for generators of $C_{0}$-groups
Haase, Markus; Rozendaal, Jan
2014-01-01
We study functional calculus properties of $C_{0}$-groups on real interpolation spaces, using transference principles. We obtain interpolation versions of the classical transference principle for bounded groups and of a recent transference principle for unbounded groups. Then we show that each group generator on a Banach space has a bounded $H^{\\infty}_{1}$-calculus on real interpolation spaces. Additional results are derived from this.
A RESULT OF SUZUKI TYPE IN PARTIAL G-METRIC SPACES
Institute of Scientific and Technical Information of China (English)
Peyman SALIMI; Pasquale VETRO
2014-01-01
Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and char-acterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric 0-completeness. In this article, we introduce the notion of partial G-metric spaces and prove a result of Suzuki type in the setting of partial G-metric spaces. We deduce also a result of common fixed point.
Sampling and Galerkin reconstruction in reproducing kernel spaces
Cheng, Cheng; Jiang, Yingchun; Sun, Qiyu
2014-01-01
In this paper, we consider sampling in a reproducing kernel subspace of $L^p$. We introduce a pre-reconstruction operator associated with a sampling scheme and propose a Galerkin reconstruction in general Banach space setting. We show that the proposed Galerkin method provides a quasi-optimal approximation, and the corresponding Galerkin equations could be solved by an iterative approximation-projection algorithm. We also present detailed analysis and numerical simulations of the Galerkin met...
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...... operators between Hilbert spaces. Fredholm operators are of interest far beyond mathematical analysis, they also play a significant role in theoretical physics, differential geometry and topology with the famous Index Theorem proved by Michael Atiyah and Isadore Singer in 1963 as a highlight. With the...... addition 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....
复指数函数系在Lpα空间中的完备性%Completeness of Complex Exponential System in Space
Institute of Scientific and Technical Information of China (English)
闫峰; 邓冠铁
2008-01-01
A necessary and sufficient condition is obtained for the complex exponential system to be dense in the weighted Banach space Lpα = {f : f∞-∞ |f(t)e-α(t)|pdt ∞}, where 1 ≤ p + ∞and α(t) is a nonnegative continuous function on R.
Approximating Fixed Points of Nonexpansive Nonself Mappings in CAT(0) Spaces
Laowang W; Panyanak B
2010-01-01
Suppose that is a nonempty closed convex subset of a complete CAT(0) space with the nearest point projection from onto . Let be a nonexpansive nonself mapping with . Suppose that is generated iteratively by , , , where and are real sequences in for some . Then -converges to some point in . This is an analog of a result in Banach spaces of Shahzad (2005) and extends a result of Dhompongsa and Panyanak (2008) to the case of nonself mappings.
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
Fixed Point Results for Multivalued Maps in Metric Spaces with Generalized Inwardness Conditions
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Frigon M
2010-01-01
Full Text Available We establish fixed point theorems for multivalued mappings defined on a closed subset of a complete metric space. We generalize Lim's result on weakly inward contractions in a Banach space. We also generalize recent results of Azé and Corvellec, Maciejewski, and Uderzo for contractions and directional contractions. Finally, we present local fixed point theorems and continuation principles for generalized inward contractions.
Cones and gauges in complex spaces : Spectral gaps and complex Perron-Frobenius theory
Rugh, Hans Henrik
2006-01-01
We introduce complex cones and associated projective gauges, generalizing a real Birkhoff cone and its Hilbert metric to complex vector spaces. We deduce a variety of spectral gap theorems in complex Banach spaces. We prove a dominated complex cone-contraction Theorem and use it to extend the classical Perron-Frobenius Theorem to complex matrices, Jentzsch's Theorem to complex integral operators, a Krein-Rutman Theorem to compact and quasi-compact complex operators and a Ruelle-Perron-Frobeni...
On weakly Radon-Nikod\\'ym compact spaces
Martínez-Cervantes, Gonzalo
2015-01-01
A compact space is said to be weakly Radon-Nikod\\'ym if it is homeomorphic to a weak*-compact subset of the dual of a Banach space not containing an isomorphic copy of $\\ell_1$. In this work we provide an example of a continuous image of a Radon-Nikod\\'ym compact space which is not weakly Radon-Nikod\\'ym. Moreover, we define a superclass of the continuous images of weakly Radon-Nikod\\'ym compact spaces and study its relation with Corson compacta and weakly Radon-Nikod\\'ym compacta.
Energy Technology Data Exchange (ETDEWEB)
Smirnov, V A [Moscow State Pedagogical University, Moscow (Russian Federation); Kuznetsova, S V; Mayorova, I V
1998-08-31
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{sub {infinity}}-structures of Stasheff to describe the cohomology of Banach algebras and locally convex algebras.
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...
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).
Proximunalty in Orlicz-bochner Function Spaces
M. Khandaqji; Khalil, R; D. Hussein
2003-01-01
A (closed) subspace $ Y$ of a Banach space $ X$ is called proximinal if for every $ x\\in X$ there exists some $ y\\in Y$ such that $ \\|x-y\\|\\le\\|x-z\\|$ for $ z\\in Y$. It is the object of this paper is to study the proximinality of $ L^\\Phi(I,Y)$ in $ L^\\Phi(I,X)$ for some class of Young's functions $ \\Phi$, where $ I$ is the unit interval. We prove (among other results) that if $ Y$ is a separable proximinal subspace of $ X$, then $ L^\\Phi(I,Y)$ is proximinal in $ L^\\Phi(I,X)$.
Diadic Baire space and continuity of weakly quasi-continuous maps(in Ukrainian
Directory of Open Access Journals (Sweden)
O. V. Maslyuchenko
2011-07-01
Full Text Available We introduce some diadic analogue of the Choquet game and a class of diadic Baire spaces which is a subclass of Baire spaces and is wider then the class Choquet spaces. We prove that for any diadic Baire space X, a Banach space Y, a countable Asplund∗ norming set E⊆Y∗ and for every map φ:X→Y, such that zφ is quasi-continuous for any z∈E, the discontinuity point set C(φ is residual.
Nice Surjections on Spaces of Operators
Indian Academy of Sciences (India)
T S S R K Rao
2006-11-01
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 $\\mathcal{K}(X, Y)$ for Banach spaces , . We give necessary and sufficient conditions when nice surjections are given by composition operators. Our results imply automatic continuity of these maps with respect to other topologies on spaces of operators. We also formulate the corresponding result for $\\mathcal{L}(X, Y)$ thereby proving an analogue of the result from [9] for $L^p(1 < p ≠ 2 < ∞)$ spaces. We also formulate results when nice operators are not of the canonical form, extending and correcting the results from [8].
Supercyclicity with Respect to a Sequence on Special Sequence Spaces
Directory of Open Access Journals (Sweden)
S. Foroutan, and B. Yousef
2007-06-01
Full Text Available Let {β(n}∞ n=−∞ be a sequence of positive numbers such that β(0 = 1 and let 1 < p < ∞. We consider the space of all formal Laurent series f(z = P∞ n=−∞ ˆf(nz n such that X∞ n=−∞ | ˆf(n| pβ(n p < ∞. We investigate the supercyclicity with respect to a sequence on the Banach spaces of formal Laurent series
Liang Yue; Yang He
2011-01-01
Abstract The paper deals with the existence of positive solutions for Neumann boundary value problems of nonlinear second-order integro-differential equations - u ″ ( t ) + M u ( t ) = f ( t , u ( t ) , ( S u ) ( t ) ) , 0 < t < 1 , u ′ ( 0 ) = u ′ ( 1 ) = θ and u ″ ( t ) + M u ( t ) = f ( t , u ( t ) , ( S u ) ( t ) ) , 0 < t < 1 , u ′ ( 0 ) ...
International Nuclear Information System (INIS)
The paper studies a class of set-values operators with emphasis on properties of their adjoints and existence of eigenvalues and eigenvectors of infinite-dimensional convex closed set-valued operators. Sufficient conditions for existence of eigenvalues and eigenvectors of set-valued convex closed operators are derived. These conditions specify possible features of control problems. The results are applied to some constrained control problems of infinite-dimensional systems described by discrete-time inclusions whose right-hand-sides are convex closed set- valued functions. (author). 8 refs
Banach空间中的∞阶Bessel序列%Bessel sequence of order ∞ in a Banach space
Institute of Scientific and Technical Information of China (English)
虞志坚; 曹怀信
2001-01-01
在Banach空间中引入了∞阶Bessel序列与 Bessel算子的概念,研究了它们的一系列重要性质,并给出了一个序列成为∞阶Bessel序列的若干充分必要条件,证明了全体∞阶Bessel序列之集构成一个Banach空间.
Bessel sequences of order 1 in a Banach space%Banach空间中的1阶Bessel序列
Institute of Scientific and Technical Information of China (English)
虞志坚; 曹怀信
2005-01-01
在Banach空间X中引入了1阶Bessel序列与Bessel算子的概念,证明了X上的全体1阶Bessel序列构成一个Banach空间;对X上的任意1阶Bessel序列f={fn}n∈∧,引入了算子Tf:X*→l1,给出一个序列成为1阶Bessel序列的若干充分必要条件;引入(1,∞)阶对偶对的概念,证明了(f,g*)成为X×X*中的(1,∞)阶对偶对当且仅当Tf*Tg*|x=IX.
Khinchin's Inequality, Dunford-Pettis and Compact Operators on the Space ([0, 1], )
Indian Academy of Sciences (India)
Dumitru Popa
2007-02-01
We prove that if , are Banach spaces, a compact Hausdorff space and :(,) → is a bounded linear operator, and if is a Dunford–Pettis operator the range of the representing measure $G()\\subseteq D P(X, Y)$ is an uniformly Dunford–Pettis family of operators and $\\|G\\|$ is continuous at $\\emptyset$. As applications of this result we give necessary and/or sufficient conditions that some bounded linear operators on the space $C([0,1],X)$ with values in $c_0$ or $l_p,(1≤ p < ∞)$ be Dunford–Pettis and/or compact operators, in which, Khinchin’s inequality plays an important role.
On $\\mathfrak{I}$-reconstruction Property
Vashisht, L. K.; Khattar, Geetika
2013-01-01
Reconstruction property in Banach spaces introduced and studied by Casazza and Christensen in [1]. In this paper we introduce reconstruction property in Banach spaces which satisfy $\\mathfrak{I}$-property. A characterization of reconstruction property in Banach spaces which satisfy $\\mathfrak{I}$-property in terms of frames in Banach spaces is obtained. Banach frames associated with reconstruction property are discussed.
ÜLGER, Ali; Lau, Anthony To-Ming
2014-01-01
Let A be a commutative Banach algebra with a BAI (=bounded approximate identity). We equip A** with the (first) Arens multiplication. To each idempotent element u of A** we associate the closed ideal I-u = {a is an element of A : au = 0} in A. In this paper we present a characterization of the closed ideals of A with BAI's in terms of idempotent elements of A**. The main results are: a) A closed ideal I of A has a BAT if there is an idempotent u is an element of A** such that I = I-u and the ...
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.
The Approximation Theorem of Convolution Operator in △p Set-valued Function Space
Institute of Scientific and Technical Information of China (English)
Pei-xin Ye
2002-01-01
The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas.We investigate the properties of p-bounded integrable random set. Based on this we endow it with △p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to △p metric. Moreover we also can establish analogous theorem for other integral type operator in △p space,
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.
Embedding and Maximal Regular Differential Operators in Sobolev-Lions Spaces
Institute of Scientific and Technical Information of China (English)
Veli B. SHAKHMUROV
2006-01-01
This study focuses on vector-valued anisotropic Sobolev-Lions spaces associated with Banach spaces E0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of spaces E0 and E. In particular, the most regular class of interpolation spaces Eα between E0, E depending on α and the order of space are found and the boundedness of differential operators Dα from this space to Eα -valued Lp,γ spaces is proved. These results are applied to partial differential-operator equationswith parameters to obtain conditions that guarantee the maximal Lp,γ regularity and R-positivity uniformly with respect to these parameters.
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...
赋β-范空间中的最佳逼近问题%The Problems of Best Approximation in β-Normed Spaces(0＜β＜1)
Institute of Scientific and Technical Information of China (English)
王见勇
2008-01-01
This paper deals with the problems of best approximation in β-normed spaces.With the tool of conjugate cone introduced in [1] and via the Hahn-Banach extension theorem of β-subseminorm in [2],the characteristics that an element in a closed subspace is the best approximation are given in Section 2.It is obtained in Section 3 that all convex sets or subspaces of a β-normed space are semi-Chebyshev if and only if the space is itself strictly convex.The fact that every finite dimensional subspace of a strictly convex β-normed space must be Chebyshev is proved at last.
A generalized preimage theorem in global analysis
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The concept of locally fine point and generalized regular valueof a C1 map between Banach spaces were carried over C1 map between Banach manifolds. Hence the preimage theorem, a principle constructing Banach manifolds in global analysis, is generalized.
Fixed Points, Inner Product Spaces, and Functional Equations
Directory of Open Access Journals (Sweden)
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.
Best simultaneous approximation in function and operator spaces
Abu-Sirhan, Eyad
2012-01-01
Let Z be a Banach space and G be a closed subspace of Z. For f1,f2 \\in Z, the distance from f1,f2 to G is defined by d(f1,f2,G) = \\underset{f \\in G}{\\inf} max {||f1-f||, ||f2-f||}. An element g\\ast \\in G satisfying max {||f1-g\\ast ||, || f2-g\\ast ||} = \\underset{f \\in G}{\\inf } max {|| f1-f||, ||f2-f||} is called a best simultaneous approximation for f1,f2 from G. In this paper, we study the problem of best simultananeous approximation in the space of all continuous X-valued fun...
International Nuclear Information System (INIS)
Precisely two coadjoint orbit spaces of the group of string reparametrizations carry in a natural way the structure of infinite dimensional, holomorphically homogeneous complex manifolds. These are M1=Diff(S1)/Rot(S1) and M2=Diff(S1)/Mo-barb(S1). M2 can be naturally considered as (embedded in) the classical univeral Teichmueller space T(Δ), simply by noting that a diffeomorphism of S1 is a quasi-symmetric homeomorphism. T(Δ) is itself a homomorphically homogeneous complex Banach manifold. We prove that the inclusion of M2 in T(Δ) is complex analytic. Every Teichmueller space of finite or infinite dimension is contained canonically and holomorphically in T(Δ). Our result thus appears to connect the loop space approach to bosonic string theory with the sum-over moduli (Polyakov path integral) approach. (author). 12 refs
On operators with bounded approximation property
Reinov, Oleg
2013-01-01
It is known that any separable Banach space with BAP is a complemented subspace of a Banach space with a basis. We show that every operator with bounded approximation property, acting from a separable Banach space, can be factored through a Banach space with a basis.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper is concerned with the existence and uniqueness of solution for a class of stochastic functional equation: X =～φ (X), where ～φ: B → B and B is a Banach space consisted of all left-continuous. (Ft)-adapted processes. Also, the main result is applied to some S.D.E (or S.I.E.). And the authors adopted some of the results in current research in the models of stochastic control recently. This paper proves the existence and uniquence and uniqueness of solution for stochastic functional equation. A series of corollaries are deduced from the special examples of the theorems in this paper.
MULTIPLIERS AND TENSOR PRODUCTS OF WEIGHTED LP-SPACES
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Let G be a locally compact uninmodular group with Haar measure rmdx and ω be the Beurling's weight function on G (Reiter, [10]). In this paper the authors define a space APωq,q (G) and prove that Aωp,q (G) is a translation invariant Banach space. Furthermore the authors discuss inclusion properties and show that if G is a locally compact abelian group then Aωp,q (G) admits an approximate identity bounded in L1ω. (G). It is also proved that the space Lpωp (G) L1ω lPω(G) is isometrically isomorphic to the space Apω.q (G) and the space of multipliers from Lωp (G) to Lqωq-1 (G) is isometrically isomorphic to the dual of the space Aωp,q (G) iff G satisfies a property Ppq. At the end of this work it is showed that if G is a locally compact abelian group then the space of all multipliers from L1ω (G) to Aωp,q (G) is the space Aωp,q (G).
Two Sufficient Conditions of Explicit Convex Functions in Banach Spaces%Banach空间中显凸泛函的两个充分条件
Institute of Scientific and Technical Information of China (English)
刘彩平
2006-01-01
在Banach空间中给出了显凸泛函的概念,然后利用泛函的G-可微性,给出了显凸泛函的两个充分条件.即如果泛函J:V→R在V中是G-可微的,且其G-微分满足1)(A)u,v∈V,J(u)≠J(v),有J(v,u-v)＜J(u)-J(V);或者2),(A)u,v∈V,J(u)≠J(v),有J'(u,u-v)-J'(v,u-v)＞0,那么J在V中是显凸的.
PERTURBATIONS OF BESSEL SEQUENCES OF ORDER 1 IN A BANACH SPACE%Banach空间中的1阶Bessel列的扰动
Institute of Scientific and Technical Information of China (English)
王秋芬; 曹怀信; 武海辉
2009-01-01
用算子论的方法讨论了Banach空间中的p(1≤p≤∞)阶Bessel列,研究了p(1＜p＜∞)阶Bessel列扰动成q阶(1/p+1/q)Bessel列的条件,并给出了1阶Bessel列扰动成1阶和∞阶Bessel列的充分条件,从而得到了一些有趣的结果.
Banach空间中Xd-Bessel列的广义扰动%GENERALIZED PERTURBATION OF Xd-BESSEL SEQUENCE IN BANACH SPACE
Institute of Scientific and Technical Information of China (English)
刘楠; 刘琴; 曹怀信
2010-01-01
运用算子理论探讨了Banach空间中Xd-Bessel列的广义扰动,首先对Banach空间X的任一Xd-Bessel列f={fi}∞i=1做一些广义扰动,得到新序列g={gi}∞i=1, 讨论了g成为Bessel列的条件, 然后用一列有界线性算子作用于f,得到另一新的序列g={gi}∞i=1,讨论了这个新序列g成为Bessel列的条件.
Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers
Directory of Open Access Journals (Sweden)
Ahmet Faruk Çakmak
2014-01-01
Full Text Available This paper is devoted to investigate some characteristic features of complex numbers and functions in terms of non-Newtonian calculus. Following Grossman and Katz, (Non-Newtonian Calculus, Lee Press, Piegon Cove, Massachusetts, 1972, we construct the field ℂ* of *-complex numbers and the concept of *-metric. Also, we give the definitions and the basic important properties of *-boundedness and *-continuity. Later, we define the space C*(Ω of *-continuous functions and state that it forms a vector space with respect to the non-Newtonian addition and scalar multiplication and we prove that C*(Ω is a Banach space. Finally, Multiplicative calculus (MC, which is one of the most popular non-Newtonian calculus and created by the famous exp function, is applied to complex numbers and functions to investigate some advance inner product properties and give inclusion relationship between C*(Ω and the set of C*′(Ω*-differentiable functions.
The approximation property of some vector valued Sobolev-Slobodeckij spaces
Directory of Open Access Journals (Sweden)
Joaquín Motos
1992-09-01
Full Text Available In this paper we consider the Sobolev-Slobodeckij spaces Wm,p(Ã¢Â„Âœn,E where E is a strict (LF-space, mÃ¢ÂˆÂˆ(0,Ã¢ÂˆÂžÃ¢Â„Â• and pÃ¢ÂˆÂˆ[1,Ã¢ÂˆÂž. We prove that Wm,p(Ã¢Â„Âœn,E has the approximation property provided E has it, furthermore if E is a Banach space with the strict approximation property then Wm,p(Ã¢Â„Âœn,E has this property.
A maximin characterization of the escape rate of nonexpansive mappings in metrically convex spaces
Gaubert, Stephane
2010-01-01
We establish a maximin characterization of the linear escape rate of the orbits of a nonexpansive mapping on a complete (hemi-)metric space, under a mild form of Busemann's nonpositive curvature condition (we require a distinguished family of geodesics with a common origin to satisfy a convexity inequality). This characterization, which involves horofunctions, generalizes the Collatz-Wielandt characterization of the spectral radius of a nonnegative matrix. It yields as corollaries a theorem of Kohlberg and Neyman (1981), concerning nonexpansive maps in Banach spaces, a variant of a Denjoy-Wolff type theorem of Karlsson (2001), together with a refinement of a theorem of Gunawardena and Walsh (2003), concerning order-preserving positively homogeneous self-maps of symmetric cones.
Djebali, Smaïl; Sahnoun, Zahira
This paper is devoted to establishing new variants of some nonlinear alternatives of Leray-Schauder and Krasnosel'skij type involving the weak topology of Banach spaces. The De Blasi measure of weak noncompactness is used. An application to solving a nonlinear Hammerstein integral equation in L spaces is given. Our results complement recent ones in [K. Latrach, M.A. Taoudi, A. Zeghal, Some fixed point theorems of the Schauder and the Krasnosel'skij type and application to nonlinear transport equations, J. Differential Equations 221 (2006) 256-2710] and [K. Latrach, M.A. Taoudi, Existence results for a generalized nonlinear Hammerstein equation on L spaces, Nonlinear Anal. 66 (2007) 2325-2333].
Fixed point theory in distance spaces
Kirk, William
2014-01-01
This is a monograph on fixed point theory, covering the purely metric aspects of the theory–particularly results that do not depend on any algebraic structure of the underlying space. Traditionally, a large body of metric fixed point theory has been couched in a functional analytic framework. This aspect of the theory has been written about extensively. There are four classical fixed point theorems against which metric extensions are usually checked. These are, respectively, the Banach contraction mapping principal, Nadler’s well known set-valued extension of that theorem, the extension of Banach’s theorem to nonexpansive mappings, and Caristi’s theorem. These comparisons form a significant component of this book. This book is divided into three parts. Part I contains some aspects of the purely metric theory, especially Caristi’s theorem and a few of its many extensions. There is also a discussion of nonexpansive mappings, viewed in the context of logical foundations. Part I also contains certain re...
Conference on Abstract Spaces and Approximation
Szökefalvi-Nagy, B; Abstrakte Räume und Approximation; Abstract spaces and approximation
1969-01-01
The present conference took place at Oberwolfach, July 18-27, 1968, as a direct follow-up on a meeting on Approximation Theory [1] held there from August 4-10, 1963. The emphasis was on theoretical aspects of approximation, rather than the numerical side. Particular importance was placed on the related fields of functional analysis and operator theory. Thirty-nine papers were presented at the conference and one more was subsequently submitted in writing. All of these are included in these proceedings. In addition there is areport on new and unsolved problems based upon a special problem session and later communications from the partici pants. A special role is played by the survey papers also presented in full. They cover a broad range of topics, including invariant subspaces, scattering theory, Wiener-Hopf equations, interpolation theorems, contraction operators, approximation in Banach spaces, etc. The papers have been classified according to subject matter into five chapters, but it needs littl...
Relativistic helicity and link in Minkowski space-time
Energy Technology Data Exchange (ETDEWEB)
Yoshida, Z.; Kawazura, Y. [Graduate School of Frontier Sciences, University of Tokyo, Kashiwanoha, Kashiwa, Chiba 277-8561 (Japan); Yokoyama, T. [Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido 060-0810 (Japan)
2014-04-15
A relativistic helicity has been formulated in the four-dimensional Minkowski space-time. Whereas the relativistic distortion of space-time violates the conservation of the conventional helicity, the newly defined relativistic helicity conserves in a barotropic fluid or plasma, dictating a fundamental topological constraint. The relation between the helicity and the vortex-line topology has been delineated by analyzing the linking number of vortex filaments which are singular differential forms representing the pure states of Banach algebra. While the dimension of space-time is four, vortex filaments link, because vorticities are primarily 2-forms and the corresponding 2-chains link in four dimension; the relativistic helicity measures the linking number of vortex filaments that are proper-time cross-sections of the vorticity 2-chains. A thermodynamic force yields an additional term in the vorticity, by which the vortex filaments on a reference-time plane are no longer pure states. However, the vortex filaments on a proper-time plane remain to be pure states, if the thermodynamic force is exact (barotropic), thus, the linking number of vortex filaments conserves.
A Moment Characterization of B-Valued Generalized Functionals of White Noise
Institute of Scientific and Technical Information of China (English)
Cai Shi WANG; Zhi Yuan HUANG
2006-01-01
Kernel theorems are established for Banach space-valued multilinear mappings. A moment characterization theorem for Banach space-valued generalized functionals of white noise is proved by using the above kernel theorems. A necessary and sufficient condition in terms of moments is given for sequences of Banach space-valued generalized functionals of white noise to converge strongly.The integration is also discussed of functions valued in the space of Banach space-valued generalized functionals.
The Compact Approximation Property does not imply the Approximation Property
Willis, George A.
1992-01-01
It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact approximation property.
Several applications of the theory of random conjugate spaces to measurability problems
Institute of Scientific and Technical Information of China (English)
2007-01-01
The central purpose of this paper is to illustrate that combining the recently developed theory of random conjugate spaces and the deep theory of Banach spaces can, indeed, solve some difficult measurability problems which occur in the recent study of the Lebesgue (or more general, Orlicz)-Bochner function spaces as well as in a slightly different way in the study of the random functional analysis but for which the measurable selection theorems currently available are not applicable. It is important that this paper provides a new method of studying a large class of the measurability problems, namely first converting the measurability problems to the abstract existence problems in the random metric theory and then combining the random metric theory and the relative theory of classical spaces so that the measurability problems can be eventually solved. The new method is based on the deep development of the random metric theory as well as on the subtle combination of the random metric theory with classical space theory.
Herbert, Dexter (Editor)
1991-01-01
In this education video series, 'Liftoff to Learning', astronauts (Bruce Melnick, Thomas Akers, William Shepherd, Robert Cabana, and Richard Richards) describe the historical beginnings of space exploration from the time of Robert H. Goddard (considered the Father of Rocketry), who, in 1929, invented the first propellant rocket, the prototype of modern liquid propellant rockets, up to the modern Space Shuttles. The questions - where is space, what is space, and how do astronauts get to, stay in, and come back from space are answered through historical footage, computer graphics, and animation. The space environment effects, temperature effects, and gravitational effects on the launching, orbiting, and descent of the Shuttles are discussed. Included is historical still photos and film footage of past space programs and space vehicles.
Peskine, Christian; Sernesi, Edoardo
1987-01-01
The main topics of the conference on "Curves in Projective Space" were good and bad families of projective curves, postulation of projective space curves and classical problems in enumerative geometry.
M Crang
2005-01-01
Spaces of Geographical Thought examines key ideas like space and place - which inform the geographic imagination. The text: discusses the core conceptual vocabulary of human geography: agency: structure; state: society; culture: economy; space: place; black: white; man: woman; nature: culture; local: global; and time: space; explains the significance of these binaries in the constitution of geographic thought; and shows how many of these binaries have been interrogated and re-imagined in more...
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 antibiotic...
DEFF Research Database (Denmark)
Berglund, Alexander
2014-01-01
We prove that a nilpotent space is both formal and coformal if and only if it is rationally homotopy equivalent to the derived spatial realization of a graded commutative Koszul algebra. We call such spaces Koszul spaces and show that the rational homotopy groups and the rational homology of...... iterated loop spaces of Koszul spaces can be computed by applying certain Koszul duality constructions to the cohomology algebra. - See more at: http://www.ams.org/journals/tran/2014-366-09/S0002-9947-2014-05935-7/#sthash.hc29cqck.dpuf...
Väth, Martin
1997-01-01
Ideal spaces are a very general class of normed spaces of measurable functions, which includes e.g. Lebesgue and Orlicz spaces. Their most important application is in functional analysis in the theory of (usual and partial) integral and integro-differential equations. The book is a rather complete and self-contained introduction into the general theory of ideal spaces. Some emphasis is put on spaces of vector-valued functions and on the constructive viewpoint of the theory (without the axiom of choice). The reader should have basic knowledge in functional analysis and measure theory.
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...
Operator Ideals arising from Generating Sequences
Wong, Ngai-Ching
2011-01-01
In this note, we will discuss how to relate an operator ideal on Banach spaces to the sequential structures it defines. Concrete examples of ideals of compact, weakly compact, completely continuous, Banach-Saks and weakly Banach-Saks operators will be demonstrated.
Institute of Scientific and Technical Information of China (English)
倪仁兴
2001-01-01
设C是实Banach空间X中有界闭凸子集且O是C的内点,G是X中非空有界闭的相对弱紧子集.记K(X)为X的非空紧凸子集并赋Hausdorff距离.称广义共同远达点问题maxc(A,G)是适定的是指它有唯一解(x0,z0)且它的每个极大化序列均强收敛到(x0,z0).在C是严格凸和Kadec的假定下,我们运用不同于De Blasi,Myjaland Papini和Li等人的方法证明了集{A∈K(X);maxc(A,G)是适定的}含有K(X)中稠Gδ集,这本质地推广和延拓了包括De Blasi,Myjak and Papini和Li等人在内的近期相应结果.
Institute of Scientific and Technical Information of China (English)
许绍元; 马丽; 谢显华
2011-01-01
利用非扩张映射的非线性二择一性质,得到了一致凸Banach空间中非扩张映射的若干新不动点定理,从而推广了著名的非扩张映射Altman定理、Roth定理和Petryshyn定理.%By means of nonlinear alternative for nonexpansive mappings, some new fixed point theorems of nonexpansive mappings are obtained. As a result,the famous Altman s theorem,Roth's theorem and Pet-ryshyn theorem for such class of mappings are generalized.
Institute of Scientific and Technical Information of China (English)
许绍元
2007-01-01
利用Banach空间中局部强伪压缩映射的一个基本不动点定理,在适当的边界条件下,得到了Banach空间中局部强伪压缩映射的新不动点定理.特别地,得到Banach空间中局部强伪压缩映射的Altman定理、Roth 定理和Petryshyn 定理,以及定理的各种推广形式.
Institute of Scientific and Technical Information of China (English)
许绍元
2011-01-01
Based on a basic result for continuous mappings satisfying Monch condition, some new fixed point theorems of continuous mappings satisfying Monch condition are obtained. As a result, the famous Altman' s theorem,Roth's theorem and Petryshyn theorem for such class of mappings are obtained and generalized.%利用Banach空间中满足Monch条件的连续映射的1个基本不动点定理,在适当的边界条件下,得到了Banach空间中满足Monch条件的连续映射的新不动点定理.特别地,得到了Banach空间中满足Monch条件的连续映射的Altman定理、Roth定理和Petryshyn定理及其各种推广形式.
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.
绝对平均有界数列空间Aab(K)%Absolutely Average Bounded Number Sequence Space Aab(K)
Institute of Scientific and Technical Information of China (English)
马凤红; 罗成; 孙凤龙
2011-01-01
Based on the absolutely average convergence of a number sequence,the concept of absolutely average bounded number sequence is given.Space Aab (K) is defined as absolutely average bounded number sequences over the real or complex scalar field K ,which is a space between space 1∞ of bounded number sequences and space Ab (K) of approxmatively bounded number sequences.Moreover,that an equivalent condition of a number sequence is absolutely average bounded is given,and space Aab(K) is a non-separable , non-reflexive Banach space which has neither the Krern-Mil 'man property nor Radon-Nikodym property are proved.%提出了绝对平均有界数列的概念,并由此定义了实(或复)数域K上绝对平均有界的数列空间Aab(K),这是一个介于有界数列空间l∞和近似有界数列空间Ab(K)之间的空间.给出了数列绝对平均有界性的等价条件,证明了空间Aab(K)是不可分的、不自反的、不具有Kre(r)n-Mil'man性质和Radon-Nikod(y)m性质的Banach空间.
Projective limits of weighted (LB) - spaces of holomorphic functions
Wegner, Sven-Ake
2010-01-01
Los límites proyectivos de límites inductivos de espacios de Banach, también llamados espacios (PLB), surgen de forma natural en el análisis matemático. En esta tesis estudiamos espacios (PLB), cuyos bloques de construcción son espacios de Banach de funciones holomorfas definidas por normas supremo ponderadas. El estudio de estos espacios extiende la investigación de Agethen, Bierstedt, Bonet quienes han considerado recientemente espacios (PLB) ponderados de funciones continuas. Desde o...
Rossi, Alessandro
2011-01-01
Space debris are all man made objects including fragments and elements thereof, in Earth orbit or re-entering the atmosphere, that are non functional. This widely accepted official definition was adopted by the Inter-Agency Space Debris Coordination Committee (IADC), an international governmental forum for the worldwide coordination of activities related to the issues of man-made and natural debris in space.
Adams, David R
2015-01-01
In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis. There are three main claims concerning these spaces that are covered: determining the integrability classes of the trace of Riesz potentials of an arbitrary Morrey function; determining the dimensions of singular sets of weak solutions of PDE (e.g. The Meyers-Elcart System); and determining whether there are any “full” interpolation results for linear operators between Morrey spaces. This book will serve as a useful reference to graduate students and researchers interested in Potential Theory, Harmonic Analysis, PDE, and/or Morrey Space Theory. .
Falmagne, Jean-Claude
2011-01-01
Learning spaces offer a rigorous mathematical foundation for practical systems of educational technology. Learning spaces generalize partially ordered sets and are special cases of knowledge spaces. The various structures are investigated from the standpoints of combinatorial properties and stochastic processes. Leaning spaces have become the essential structures to be used in assessing students' competence of various topics. A practical example is offered by ALEKS, a Web-based, artificially intelligent assessment and learning system in mathematics and other scholarly fields. At the heart of A
National Aeronautics and Space Administration, Huntsville, AL. George C. Marshall Space Flight Center.
This pamphlet describes the Space Telescope, an unmanned multi-purpose telescope observatory planned for launch into orbit by the Space Shuttle in the 1980s. The unique capabilities of this telescope are detailed, the major elements of the telescope are described, and its proposed mission operations are outlined. (CS)
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
DEFF Research Database (Denmark)
Svaneklink, Annette
2009-01-01
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...
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.
Armstrong, Drew; Rhoades, Brendon
2012-01-01
Let $W$ be a Weyl group with root lattice $Q$ and Coxeter number $h$. The elements of the finite torus $Q/(h+1)Q$ are called the $W$-{\\sf parking functions}, and we call the permutation representation of $W$ on the set of $W$-parking functions the (standard) $W$-{\\sf parking space}. Parking spaces have interesting connections to enumerative combinatorics, diagonal harmonics, and rational Cherednik algebras. In this paper we define two new $W$-parking spaces, called the {\\sf noncrossing parking space} and the {\\sf algebraic parking space}, with the following features: 1) They are defined more generally for real reflection groups. 2) They carry not just $W$-actions, but $W\\times C$-actions, where $C$ is the cyclic subgroup of $W$ generated by a Coxeter element. 3) In the crystallographic case, both are isomorphic to the standard $W$-parking space. Our Main Conjecture is that the two new parking spaces are isomorphic to each other as permutation representations of $W\\times C$. This conjecture ties together sever...
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...
Hausmann, Jean-Claude; Holm, Tara; Puppe, Volker
2005-01-01
There are classical examples of spaces X with an involution tau whose mod 2-comhomology ring resembles that of their fixed point set X^tau: there is a ring isomorphism kappa: H^2*(X) --> H^*(X^tau). Such examples include complex Grassmannians, toric manifolds, polygon spaces. In this paper, we show that the ring isomorphism kappa is part of an interesting structure in equivariant cohomology called an H^*-frame. An H^*-frame, if it exists, is natural and unique. A space with involution admitti...
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.
Pool, Sam L.
1988-01-01
This paper attempts to underscore the importance of continued studies on the effects of space on human physiology. With particular reference to the Space Station, it is pointed out that there are two aspects which are challenging to life scientists: first is the development of a research capability for the life sciences which will be used to conduct investigations necessary to extend the time humans can remain in space; second is the challenge to develop a medical capability to provide prevention, diagnosis, and therapy. A discussion of physiological changes that have been observed in spacecrews follows along the lines of the two aspects mentioned.
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.
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.
Rigby, Jane R.
2011-01-01
The science of astronomy depends on modern-day temples called telescopes. Astronomers make pilgrimages to remote mountaintops where these large, intricate, precise machines gather light that rains down from the Universe. Bit, since Earth is a bright, turbulent planet, our finest telescopes are those that have been launched into the dark stillness of space. These space telescopes, named after heroes of astronomy (Hubble, Chandra, Spitzer, Herschel), are some of the best ideas our species has ever had. They show us, over 13 billion years of cosmic history, how galaxies and quasars evolve. They study planets orbiting other stars. They've helped us determine that 95% of the Universe is of unknown composition. In short, they tell us about our place in the Universe. The next step in this journey is the James Webb Space Telescope, being built by NASA, Europe, and Canada for a 2018 launch; Webb will reveal the first galaxies that ever formed.
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 of...
Boucher, M.-P.
2014-04-01
This paper looks at earthly architectural applications of scientific research on space orientation in reduced gravity conditions. It asks how unprecedented forms of perception experienced in reduced gravity conditions give rise to unconventional modes of living. Looking at different technical lineages for achieving weightlessness: on the one hand, outer space exploration and its habitats, and on the other, technologies of suspension associated with experimental architecture, it questions the pragmatics of exchangeability between art and science. Instead of insisting on systems of valuation, that is, instead of opposing the functionality of outer space habitats with the aesthetic of experimental architecture, both practices will be approached in their own terms and on their terrain, that is, in the pragmatics of their effectiveness.
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...
DEFF Research Database (Denmark)
Fajstrup, Lisbeth; Goubault, Eric; Haucourt, Emmanuel;
2012-01-01
State-space reduction techniques, used primarily in model-checkers, all rely on the idea that some actions are independent, hence could be taken in any (respective) order while put in parallel, without changing the semantics. It is thus not necessary to consider all execution paths in the...... concurrent languages, where programs are interpreted as directed topological spaces, and study its properties in order to devise an algorithm for computing dihomotopy classes of execution paths. In particular, our algorithm is able to compute a control-flow graph for concurrent programs, possibly containing...
Cort, Cliff
2006-01-01
Education administrators face the dual dilemma of crowded, aging facilities and tightening capital budgets. The challenge is to build the necessary classroom, laboratory and activity space while minimizing the length and expense of the construction process. One solution that offers an affordable alternative is modular construction, a method that…
2005-01-01
An old water tank from the time of the ISR is being converted into a temporary store for ATLAS muon chambers. This is the last chapter in the big programme by the PH Department to make better use of space at CERN.
Roberts, Lisa
2005-01-01
This viewgraph presentation summarizes changes to the Space Shuttle Propulsions Systems made for the Return to Flight in response to the recommendations of the Columbia Accident Investigation Board (CAIB). The presentation also includes an overivew of the Columbia debris recovery effort.
Institute of Scientific and Technical Information of China (English)
2010-01-01
@@ One day after NASA brougnt the shuttle Discovery back form low Earth orbit,a Private company plans to announce a more audacious(1)v__,a tourist trip around the Moon. Space Adventrues,an American company ,has already sent two (A)t__into orbit.
Second Symposium on Space Industrialization. [space commercialization
Jernigan, C. M. (Editor)
1984-01-01
The policy, legal, and economic aspects of space industrialization are considered along with satellite communications, material processing, remote sensing, and the role of space carriers and a space station in space industrialization.
Derivations in semiprime rings and Banach algebras
Directory of Open Access Journals (Sweden)
Shervin Sahebi
2014-07-01
Full Text Available Let $R$ be a $2$-torsion free semiprime ring with extendedcentroid $C$, $U$ the Utumi quotient ring of $R$ and$m, n>0$ are fixed integers. We show that if $ R $ admitsderivation $d$ such that $b[[d(x, x]_n,[y, d(y]_m]=0$for all $x, y \\in R$ where $0\
Namioka spaces and strongly Baire spaces
Mykhaylyuk, V. V.
2016-01-01
A notion of strongly Baire space is introduced. Its definition is a transfinite development of some equivalent reformulation of the Baire space definition. It is shown that every strongly Baire space is a Namioka space and every $\\beta-\\sigma$-unfavorable space is a strongly Baire space.
Free spaces over some proper metric spaces
Dalet, Aude
2014-01-01
We prove that the Lipschitz-free space over a countable proper metric space is isometric to a dual space and has the metric approximation property. We also show that the Lipschitz-free space over a proper ultrametric space is isometric to the dual of a space which is isomorphic to c_0.
Smith, Scott M.
2009-01-01
Optimal nutrition will be critical for crew members who embark on space exploration missions. Nutritional assessment provides an opportunity to ensure that crewmembers begin their missions in optimal nutritional status, to document changes during a mission and, if necessary, to provide intervention to maintain that status throughout the mission, and to assesses changes after landing in order to facilitate the return to their normal status as soon as possible after landing. We report here the findings from our nutritional assessment of astronauts who participated in the International Space Station (ISS) missions, along with flight and ground-based research findings. We also present ongoing and planned nutrition research activities. These studies provide evidence that bone loss, compromised vitamin status, and oxidative damage are the critical nutritional concerns for space travelers. Other nutrient issues exist, including concerns about the stability of nutrients in the food system, which are exposed to longterm storage and radiation during flight. Defining nutrient requirements, and being able to provide and maintain those nutrients on exploration missions, will be critical for maintaining crew member health.
Humans in Space &Space Biology
Legner, Klaus
Inevitably, members of the human species will again walk on the face of the moon and ultimately establish a permanently occupied lunar base. Also, inevitably, humans will venture to the planets within the solar system, most likely beginning with Mars or the Martian satellite, Phobos. These missions will take place because the species that contemplates them is driven by an insatiable desire for knowledge and understanding and because the technical means to accomplish these objectives are possible. There is no question that humans will establish outposts on Earth's moon and make interplanetary journeys. The only uncertainties concern when and how these expeditions are to be made. Just as a 90- or 120-day tour onboard an international space station is fundamentally different from a brief space shuttle mission; a one-year lunar base tour or a two- or three-year mission to Mars will be unique. Despite superficial similarities to other space missions and analogues, the extended durations and astronomical distances involved in lunar and Martian missions will make these activities far more difficult and dangerous. Crowded conditions, language and cultural differences, logistics problems, radiation concerns, communications lag times, workloads, and a variety of additional issues will conspire to impair the performance and affect the behaviour of long duration crew personnel. Above all stressors, however, the durations of the missions will impose the greatest burdens and extract the most severe tolls on the humans involved. On long-duration space missions, time will be the factor that can compound all issues, however trivial, into serious problems.
Wotring, Virginia E
2012-01-01
“Space Pharmacology” is a review of the current knowledge regarding the use of pharmaceuticals during spaceflights. It is a comprehensive review of the literature, addressing each area of pharmacokinetics and each major physiological system in turn. Every section begins with a topic overview, and is followed by a discussion of published data from spaceflight, and from ground experiments meant to model the spaceflight situation. Includes a discussion looking forward to the new medical challenges we are likely to face on longer duration exploration missions. This book is a snapshot of our current knowledge that also highlights areas of unknown.
International Nuclear Information System (INIS)
36 years ago, the Soviet Union sent the first space satellite, Sputnik 1, into its orbit. Since then, the number of satellites has been increasing continuous by. As a result, the atmospheric layers close to the earth are littered with debris from broken satellites and rockets. This includes about 30 abandoned nuclear reactions orbiting at a height of about 1000 km. The expected life of the reactors is higher than the half-life after which the activity level of the radioactive material will have fallen to a tolerable level. (orig./HP)
90, Sol
2008-01-01
Space Exploration, is one book in the Britannica Illustrated Science Library Series that is correlated to the science curriculum in grades 5-8. The Britannica Illustrated Science Library is a visually compelling set that covers earth science, life science, and physical science in 16 volumes. Created for ages 10 and up, each volume provides an overview on a subject and thoroughly explains it through detailed and powerful graphics-more than 1,000 per volume-that turn complex subjects into information that students can grasp. Each volume contains a glossary with full definitions for vocabulary
Space weather and space anomalies
Directory of Open Access Journals (Sweden)
L. I. Dorman
2005-11-01
Full Text Available A large database of anomalies, registered by 220 satellites in different orbits over the period 1971-1994 has been compiled. For the first time, data from 49 Russian Kosmos satellites have been included in a statistical analysis. The database also contains a large set of daily and hourly space weather parameters. A series of statistical analyses made it possible to quantify, for different satellite orbits, space weather conditions on the days characterized by anomaly occurrences. In particular, very intense fluxes (>1000 pfu at energy >10 MeV of solar protons are linked to anomalies registered by satellites in high-altitude (>15000 km, near-polar (inclination >55° orbits typical for navigation satellites, such as those used in the GPS network, NAVSTAR, etc. (the rate of anomalies increases by a factor ~20, and to a much smaller extent to anomalies in geostationary orbits, (they increase by a factor ~4. Direct and indirect connections between anomaly occurrence and geomagnetic perturbations are also discussed.
DEFF Research Database (Denmark)
Kristiansen, Erik
2015-01-01
When we play games of any kind, from tennis to board games, it is easy to notice that games seem to be configured in space, often using stripes or a kind of map on a board. Some games are clearly performed within this marked border, while it may be difficult to pinpoint such a border in games like...... hide-and-seek, but even these games are still spatially configured. The border (visible or not) both seem to separate and uphold the game that it is meant for. This chapter sets out to analyse the possible border that separates a game from the surrounding world. Johan Huizinga noted this “separateness......” in his classic work “Homo Ludens” (Huizinga 1938, translated into English 1971). This has since been developed into the concept of the “magic circle” by Salen and Zimmerman (2003), as an understanding of playing games as a kind of alternate reality. When a person cross the magic circle of a game, he...
Space Science in Action: Space Exploration [Videotape].
1999
In this videotape recording, students learn about the human quest to discover what is out in space. Students see the challenges and benefits of space exploration including the development of rocket science, a look back at the space race, and a history of manned space travel. A special section on the Saturn V rocket gives students insight into the…
Large size space construction for space exploitation
Kondyurin, Alexey
2016-07-01
Space exploitation is impossible without large space structures. We need to make sufficient large volume of pressurized protecting frames for crew, passengers, space processing equipment, & etc. We have to be unlimited in space. Now the size and mass of space constructions are limited by possibility of a launch vehicle. It limits our future in exploitation of space by humans and in development of space industry. Large-size space construction can be made with using of the curing technology of the fibers-filled composites and a reactionable matrix applied directly in free space. For curing the fabric impregnated with a liquid matrix (prepreg) is prepared in terrestrial conditions and shipped in a container to orbit. In due time the prepreg is unfolded by inflating. After polymerization reaction, the durable construction can be fitted out with air, apparatus and life support systems. Our experimental studies of the curing processes in the simulated free space environment showed that the curing of composite in free space is possible. The large-size space construction can be developed. A project of space station, Moon base, Mars base, mining station, interplanet space ship, telecommunication station, space observatory, space factory, antenna dish, radiation shield, solar sail is proposed and overviewed. The study was supported by Humboldt Foundation, ESA (contract 17083/03/NL/SFe), NASA program of the stratospheric balloons and RFBR grants (05-08-18277, 12-08-00970 and 14-08-96011).
Taha Yasin Ozturk; Sadi Bayramov
2014-01-01
Various soft topologies are being introduced on a given function space soft topological spaces. In this paper, soft compact-open topology is defined in functional spaces of soft topological spaces. Further, these functional spaces are studied and interrelations between various functional spaces with soft compact-open topology are established.
Institute of Scientific and Technical Information of China (English)
2008-01-01
The international community should join forces to avoid possible conflicts in space Military competition and conflict in outer space can be divided into three stages:militarization,wea- ponization and the space battle- field. Space militarization has become a thing of the past.Now,many countries are re- searching more advanced space weaponry technology,which means space weapon- ization is becoming a growing reality.The process of space competition is astonishingly
DEFF Research Database (Denmark)
Schmidt, Ulrik
Atmosphere and Ambient Space This paper explores the relation between atmosphere and ambient space. Atmosphere and ambient space share many salient properties. They are both ontologically indeterminate, constantly varying and formally diffuse and they are both experienced as a subtle, non......-signifying property of a given space. But from a certain point of view, the two concepts also designate quite dissimilar experiences of space. To be ’ambient’ means to surround. Accordingly, ambient space is that space, which surrounds something or somebody. (Gibson 1987: 65) Since space is essentially...... of a surrounding character, all space can thus be described as having a fundamentally ambient character. So what precisely is an ambient space, then? As I will argue in my presentation, ambient space is a sensory effect of spatiality when a space is experienced as being particularly surrounding: a ‘space effect...
Quantum Homogeneous Spaces as Quantum Quotient Spaces
Brzezinski, Tomasz
1995-01-01
We show that certain embeddable homogeneous spaces of a quantum group that do not correspond to a quantum subgroup still have the structure of quantum quotient spaces. We propose a construction of quantum fibre bundles on such spaces. The quantum plane and the general quantum two-spheres are discussed in detail.
From Physical Space to Visual Image Space
Institute of Scientific and Technical Information of China (English)
YE Zetian; LIN Hui; LIU Xianlin
2003-01-01
The theoretical framework of visual simulation in virtual reality is discussed. The new concept of visual image space is supposed. On the basis of visual image space, in visual perceptive sense, VR is considered as a spatial simulation. The objective of the spatial simulation is to transform physical space to visual image space.Last, the prototype system, surveying & mapping virtual Reality (SMVR),is developed, and the space simulation above is realized. By use of SMVR,the real 3D representation, 3D visual analysis, virtual plan and designs can be implemented.
Fundamentals of space medicine
Clément, Gilles
2011-01-01
This book details the findings from life science experiments conducted during and after space missions. It looks at the future of human space flight and what comes next, especially in the areas of planetary exploration and space tourism.
International Nuclear Information System (INIS)
The authors briefly discusses the radiation environment in near-earth space and it's influences on material, and electronic devices using in space airship, also, the research developments in space radiation effects are introduced
Energy Technology Data Exchange (ETDEWEB)
Arif, H.; Barbosa, H.; Bardet, C.; Baroud, M.; Behar, A.; Berrier, K.; Berthe, P.; Bertrand, R.; Bibyk, I.; Bisson, J.; Bloch, L.; Bobadilla, G.; Bourque, D.; Bush, L.; Carandang, R.; Chiku, T.; Crosby, N.; De Seixas, M.; De Vries, J.; Doll, S.; Dufour, F.; Eckart, P.; Fahey, M.; Fenot, F.; Foeckersperger, S.; Fontaine, J.E.; Fowler, R.; Frey, H.; Fujio, H.; Gasa, J.M.; Gleave, J.; Godoe, J.; Green, I.; Haeberli, R.; Hanada, T.; Ha
1992-08-01
Information pertaining to the Space Solar Power Program is presented on energy analysis; markets; overall development plan; organizational plan; environmental and safety issues; power systems; space transportation; space manufacturing, construction, operations; design examples; and finance.
Bin Qin
2014-01-01
Relationships between fuzzy relations and fuzzy topologies are deeply researched. The concept of fuzzy approximating spaces is introduced and decision conditions that a fuzzy topological space is a fuzzy approximating space are obtained.
Directory of Open Access Journals (Sweden)
Yekini Shehu
2011-01-01
and strictly convex real Banach space with Kadec-Klee property using the properties of generalized f-projection operator. Using this result, we discuss strong convergence theorem concerning variational inequality and convex minimization problems in Banach spaces. Our results extend many known recent results in the literature.
Operator calculus on the class of Sato's hyperfunctions
Directory of Open Access Journals (Sweden)
Patra M.I.
2013-06-01
Full Text Available We construct a functional calculus for generators of analytic semigroupsof operators on a Banach space. The symbol class of the calculusconsists of hyperfunctions with a compact support in $[0, infty$. Domain of constructedcalculus isdense in the Banach space.
Functional calculus for generators of analytic semigroups of operators
Lopushansky O.V.; Sharyn S.V.
2012-01-01
We construct a functional calculus for generators of one-parameter boundedanalytic semigroups of operators on a Banach space. The calculus symbol classconsist of the Laplace image of the convolution algebra $cal S'_+$ of tempereddistributions with supports in $[0, infty)$. Domain of constructed calculus isdense in the Banach space.
Functional calculus for generators of analytic semigroups of operators
Directory of Open Access Journals (Sweden)
Lopushansky O.V.
2012-06-01
Full Text Available We construct a functional calculus for generators of one-parameter boundedanalytic semigroups of operators on a Banach space. The calculus symbol classconsist of the Laplace image of the convolution algebra $cal S'_+$ of tempereddistributions with supports in $[0, infty$. Domain of constructed calculus isdense in the Banach space.
Urban (space) design and space environmental management
International Nuclear Information System (INIS)
A 'convex space' has been taken as the basic unit of urban space and with a sampling of convex spaces spread all over the study area constitute a representation of the whole public urban space in the built form, in this case the CBD of Nairobi. A space is said to be convex when a straight line drawn from any point in the space to any other point in the space does not go outside the boundary of the space itself. Therefore any convex space is said to be a standard space that can be compared with another. The empirical investigation has employed several data collection methods and techniques. By aid of statistical package for social scientist, the research has adopted the multiple regression model and in turn several models that significantly explain the variation of each environmental problem have been developed and documented. These models are significant at 95 degrees significant level. This proves that urban environment has a relationship with urban design, hence the research has accepted the alternative hypothesis that a relationship exists between design and urban environmental management. Through synthesis, independent variables explaining the dependent variables have been sorted out into urban patterns. These urban patterns have further been discussed in the light of developing sustainable city environments. (author)
Chistyakov, Vyacheslav
2015-01-01
Aimed toward researchers and graduate students familiar with elements of functional analysis, linear algebra, and general topology; this book contains a general study of modulars, modular spaces, and metric modular spaces. Modulars may be thought of as generalized velocity fields and serve two important purposes: generate metric spaces in a unified manner and provide a weaker convergence, the modular convergence, whose topology is non-metrizable in general. Metric modular spaces are extensions of metric spaces, metric linear spaces, and classical modular linear spaces. The topics covered include the classification of modulars, metrizability of modular spaces, modular transforms and duality between modular spaces, metric and modular topologies. Applications illustrated in this book include: the description of superposition operators acting in modular spaces, the existence of regular selections of set-valued mappings, new interpretations of spaces of Lipschitzian and absolutely continuous mappings, the existe...
In Outer Space without a Space Suit?
Bolonkin, Alexander
2008-01-01
The author proposes and investigates his old idea - a living human in space without the encumbrance of a complex space suit. Only in this condition can biological humanity seriously attempt to colonize space because all planets of Solar system (except the Earth) do not have suitable atmospheres. Aside from the issue of temperature, a suitable partial pressure of oxygen is lacking. In this case the main problem is how to satiate human blood with oxygen and delete carbonic acid gas (carbon dioxide). The proposed system would enable a person to function in outer space without a space suit and, for a long time, without food. That is useful also in the Earth for sustaining working men in an otherwise deadly atmosphere laden with lethal particulates (in case of nuclear, chemical or biological war), in underground confined spaces without fresh air, under water or a top high mountains above a height that can sustain respiration.
In Outer Space without a Space Suit?
Bolonkin, Alexander
2008-01-01
The author proposes and investigates his old idea - a living human in space without the encumbrance of a complex space suit. Only in this condition can biological humanity seriously attempt to colonize space because all planets of Solar system (except the Earth) do not have suitable atmospheres. Aside from the issue of temperature, a suitable partial pressure of oxygen is lacking. In this case the main problem is how to satiate human blood with oxygen and delete carbonic acid gas (carbon diox...
Harris, Watson
2011-01-01
There are many articles about space management, including those that discuss space calculations, metrics, and categories. Fewer articles discuss the space budgeting processes used by administrators to allocate space. The author attempts to fill this void by discussing her administrative experiences with Middle Tennessee State University's (MTSU)…
Johnson, R. D.
1977-01-01
Organic cosmochemistry, organic materials in space exploration, and biochemistry of man in space are briefly surveyed. A model of Jupiter's atmosphere is considered, and the search for organic molecules in the solar system and in interstellar space is discussed. Materials and analytical techniques relevant to space exploration are indicated, and the blood and urine analyses performed on Skylab are described.
Space Physiology and Operational Space Medicine
Scheuring, Richard A.
2009-01-01
The objectives of this slide presentation are to teach a level of familiarity with: the effects of short and long duration space flight on the human body, the major medical concerns regarding future long duration missions, the environmental issues that have potential medical impact on the crew, the role and capabilities of the Space Medicine Flight Surgeon and the environmental impacts experienced by the Apollo crews. The main physiological effects of space flight on the human body reviewed in this presentation are: space motion sickness (SMS), neurovestibular, cardiovascular, musculoskeletal, immune/hematopoietic system and behavioral/psycho-social. Some countermeasures are discussed to these effects.
Space Based Radar To Observe Space Debris
Tolkachev, A.A.; Zolotarev, M.M.; Loukiaschenko, V.I.; Raikunov, G.G.; Yaremenko, A.I.
1998-01-01
Space debris of 1÷3mm size is known to be hazardous for astronauts and space vehicles. At the same time the possibility to notice such objects by ground based optical and radar devices in the nearest future is rather problematic. Here we propose an idea of space radar for observation of cicumterrestrial space debris. The radar works in short wave part of millimetre band, which is mostly suitable for this purpose. The radar provides detecting and tracking of 1mm size objects within 40000m2 are...
Morrison, D. R. (Compiler)
1977-01-01
Proceedings are presented of the 1976 NASA Colloquium on bioprocessing in space. The program included general sessions and formal presentations on the following topics: NASA's Space Shuttle, Spacelab, and space-processing programs; the known unusual behavior of materials in space; space-processing experiment results; cell biology, gravity sensors in cells, space electrophoresis of living cells, new approaches to biosynthesis of biologicals from cell culture in space, and zero-g fermentation concepts; and upcoming flight opportunities and industrial application planning studies already underway.
Triebel, Hans
1983-01-01
The book deals with the two scales Bsp,q and Fsp,q of spaces of distributions, where -8spaces, such as Hölder spaces, Zygmund classes, Sobolev spaces, Besov spaces, Bessel-potential spaces, Hardy spaces and spaces of BMO-type. It is the main aim of this book to give a unified treatment of the corresponding spaces on the Euclidean n-space Rn in the framework of Fourier analysis, which is based on the technique of maximal functions, Fourier multipliers and interpolation assertions. These topics are treated in Chapter 2, which is the heart
Hyperbolic spaces in Teichm\\"uller spaces
Leininger, Christopher J
2011-01-01
We prove, for any n, that there is a closed connected orientable surface S so that the hyperbolic space H^n almost-isometrically embeds into the Teichm\\"uller space of S, with quasi-convex image lying in the thick part. As a consequence, H^n quasi-isometrically embeds in the curve complex of S.
SpaceTech—Postgraduate space education
de Bruijn, Ferdi J.; Ashford, Edward W.; Larson, Wiley J.
2008-07-01
SpaceTech is a postgraduate program geared primarily for mid-career space professionals seeking to gain or improve their expertise in space systems engineering and in business engineering. SpaceTech provides a lifelong impact on its participants by broadening their capabilities, encouraging systematic "end-to-end" thinking and preparing them for any technical or business-related engineering challenges they may encounter. This flexible 1-year program offers high competency gain and increased business skills. It is held in attractive locations in a flexible, multi-cultural environment. SpaceTech is a highly effective master's program certified by the esteemed Technical University of Delft (TUD), Netherlands. SpaceTech provides expert instructors who place no barriers between themselves and participants. The program combines innovative and flexible new approaches with time-tested methods to give participants the skills required for future missions and new business, while allowing participants to meet their work commitments at the same time as they study for their master's degree. The SpaceTech program is conducted in separate sessions, generally each of 2-week duration, separated by periods of some 6-8 weeks, during which time participants may return to their normal jobs. It also includes introductory online course material that the participants can study at their leisure. The first session is held at the TUD, with subsequent sessions held at strategic space agency locations. By participating at two or more of these sessions, attendees can earn certificates of satisfactory completion from TU Delft. By participating in all of the sessions, as well as taking part in the companion Central Case Project (CCP), participants earn an accredited and highly respected master's degree in Space Systems Engineering from the TUD. Seven distinct SpaceTech modules are provided during these sessions: Space Mission Analysis and Design, Systems Engineering, Business Engineering
New pre-dual space of Morrey space
Gogatishvili, A. (Amiran); Mustafayev, R. Ch.
2013-01-01
In this paper we give new characterization of the classical Morrey space. Complementary global Morrey-type spaces are introduced. It is proved that for particular values of parameters these spaces give new pre-dual space of the classical Morrey space. We also show that our new pre-dual space of the Morrey space coincides with known pre-dual spaces.
New characterizations of Hajlasz-Sobolev spaces on metric spaces
Institute of Scientific and Technical Information of China (English)
YANG; Dachun(杨大春)
2003-01-01
This paper introduces the fractional Sobolev spaces on spaces of homogeneous type, includingmetric spaces and fractals. These Sobolev spaces include the well-known Hajfasz-Sobolev spaces as specialmodels. The author establishes various characterizations of (sharp) maximal functions for these spaces. Asapplications, the author identifies the fractional Sobolev spaces with some Lipscitz-type spaces. Moreover,some embedding theorems are also given.
DEFF Research Database (Denmark)
Lykke-Olesen, Andreas
2006-01-01
This Ph.D. dissertation takes its offset in the migration of technology and computing power into our physical environment. The consequence of this movement, termed ubiquitous computing (Wieser, 1991), is a new relationship between humans, technology and spaces. In this new context, I seek...... to conceptualize space as more than the physical container for human activity. I do this by investigating space as interface. Based on a theory of space and place set forth by Tuan (Tuan, 1977), and informed by an explorative research approach, I make the distinction between space and place as a Euclidian space...... and a Phenomenological experienced place. In this perspective, place is created by humans as they appropriate space in investing it with emotions and memories and hereby making it meaningful. Space consists of formable physical and digital space, whereas place is made up by four dimensions relating to personal, physical...
Institute of Scientific and Technical Information of China (English)
China National Space Administration
2004-01-01
@@ Currently, space activities are very active around the world. Space technologies continuously expand to various areas of human activities, and space technology and applications are becoming an indispensable part of modern information society,while the development of space science brings a brand-new view to the development of science and technology. The development of space law is not only an important approach to improving people' s quality of lives, expanding the living space of human being, and exploiting new resources, but also an important symbol of the comprehensive strength and civilization of a nation.
Institute of Scientific and Technical Information of China (English)
YAO BIN
2011-01-01
With the successful launch of Tiangong-I (Heavenly Palace -I)unmanned module on September 29,China took a significant step forward in realizing its ambitions in space.China's manned space program consists of three steps.The first step,to send an astronaut into space,was achieved in 2003.The second step,to realize multi-person space flight for extended periods of time,has been fulfilled twice.During China's third manned space flight in 2008,Chinese astronauts walked in space.
DEFF Research Database (Denmark)
Bank, Mads; Nissen, Morten
2015-01-01
The article articulates experiments with spatial constructions in two Danish social work agencies, basing on a) a sketchy genealogical reconstruction of conceptualisations and uses of space in social work and counselling; b) a search for theoretical resources to articulate new spaces, and c) data...... from a long-standing collaboration with the social workers. Beside the classical disciplinary and pastoral spaces, we find spaces of attunement, spaces of production, and public spaces as forms of spatialisations which might be taken as prototypical in attempts to develop social work and counselling....
DEFF Research Database (Denmark)
Raussen, Martin
2007-01-01
Directed spaces are the objects of study within directed algebraic topology. They are characterised by spaces of directed paths associated to a source and a target, both elements of an underlying topological space. The algebraic topology of these path spaces and their connections are studied from a...... categorical perspective. In particular, we study the preorder category associated to a directed space and various "quotient" categories arising from algebraic topological functors. Furthermore, we propose and study a new notion of directed homotopy equivalence between directed spaces....
Amir-Moez, A R; Sneddon, I N
1962-01-01
Elements of Linear Space is a detailed treatment of the elements of linear spaces, including real spaces with no more than three dimensions and complex n-dimensional spaces. The geometry of conic sections and quadric surfaces is considered, along with algebraic structures, especially vector spaces and transformations. Problems drawn from various branches of geometry are given.Comprised of 12 chapters, this volume begins with an introduction to real Euclidean space, followed by a discussion on linear transformations and matrices. The addition and multiplication of transformations and matrices a
Stereotype locally convex spaces
Energy Technology Data Exchange (ETDEWEB)
Akbarov, S S
2000-08-31
We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.
Stereotype locally convex spaces
Akbarov, S. S.
2000-08-01
We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.
Stereotype locally convex spaces
International Nuclear Information System (INIS)
We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis
DEFF Research Database (Denmark)
Bjerrum, Peter; Olsen, Kasper Nefer
2001-01-01
Inform@ed space Sensorial Perception And Computer Enchancement - bidrag til Nordisk Arkitekturforskningsforenings IT-konference, AAA april 2001.......Inform@ed space Sensorial Perception And Computer Enchancement - bidrag til Nordisk Arkitekturforskningsforenings IT-konference, AAA april 2001....
Tarver, William J.
2012-01-01
Learning Objectives are: (1) Understand the unique work environment of astronauts. (2) Understand the effect microgravity has on human physiology (3) Understand how NASA Space Medicine Division is mitigating the health risks of space missions.
National Aeronautics and Space Administration — NASA has released a series of space sounds via sound cloud. We have abstracted away some of the hassle in accessing these sounds, so that developers can play with...
Chinese Space Insurance Opportunities
Institute of Scientific and Technical Information of China (English)
LiuJie
2005-01-01
Jiang Tai Insurance Broker Co., Ltd and China Pacific Insurance (group) Co., Ltd jointly held a conference on Space and Space Insurance on January 13 and 14, 2005. About 50 representatives from 30 domestic insurance companies attended the event.
National Oceanic and Atmospheric Administration, Department of Commerce — Collection includes presentation materials and outputs from operational space environment models produced by the NOAA Space Weather Prediction Center (SWPC) and...
Computational space flight mechanics
Weiland, Claus
2010-01-01
Computational Space Flight Mechanics presents numerical solutions for topics and problems within space flight mechanics. Topics include orbit determination, Lagrange's perturbation equations for disturbed Earth's orbits, the flight of a mass point in flight path coordinates, and more.
Technology Enhanced Learning Spaces
Specht, Marcus
2016-01-01
Today’s tools and learning environments are often not designed for supporting situated, social, and mobile learning experiences and linking them to real world experiences. The talk will discuss some of the approaches for linking information space and real world space with new technology. By linking instruction, information and context in formal and informal learning spaces research on the effects of such technology enhanced learning spaces will be presented and it’s adoption and effects will ...
DEFF Research Database (Denmark)
Nilsson, Jørgen Fischer
Conceptual spaces have been proposed as topological or geometric means for establishing conceptual structures and models. This paper, after briey reviewing conceptual spaces, focusses on the relationship between conceptual spaces and logical concept languages with operations for combining concepts...... to form concepts. Speci cally is introduced an algebraic concept logic, for which conceptual spaces are installed as semantic domain as replacement for, or enrichment of, the traditional....
Okino, C.; Kwong, W.; Pang, Jackson; Gao, Jerry; Clare, L.
2006-01-01
This viewgraph presentation reviews Voice over Internet Protocol (VOIP) over a space networking environment. The topics include: 1) Drivers for VOIP in Space; 2) Challenges in the Space Networking Environment: Long Latencies, Path errors, Simplex paths, Asymmetric paths, QoS requirements, Team-based operations, and Overhead concerns; 3) Possible VOIPOSN approaches; 4) Study of BER, code type and voice frame length on PESQ-MOS; 5) Codec Latency Trade Space; and 6) Testbed.
Konishi, Masakazu
2003-01-01
Behavioral, anatomical, and physiological approaches can be integrated in the study of sound localization in barn owls. Space representation in owls provides a useful example for discussion of place and ensemble coding. Selectivity for space is broad and ambiguous in low-order neurons. Parallel pathways for binaural cues and for different frequency bands converge on high-order space-specific neurons, which encode space more precisely. An ensemble of broadly tuned place-coding neurons may conv...
Space tourism risks: A space insurance perspective
Bensoussan, Denis
2010-06-01
Space transportation is inherently risky to humans, whether they are trained astronauts or paying tourists, given that spaceflight is still in its relative infancy. However, this is easy to forget when subjected to the hype often associated with space tourism and the ventures seeking to enter that market. The development of commercial spaceflight constitutes a challenge as much as a great opportunity to the insurance industry as new risks emerge and standards, policies and procedures to minimise/mitigate and cover them still to be engineered. Therefore the creation of a viable and affordable insurance regime for future space tourists is a critical step in the development of a real space tourism market to address burning risk management issues that may otherwise ultimately hamper this nascent industry before it has a chance to prove itself.
On generalized topological spaces
Piȩkosz, Artur
2009-01-01
In this paper a systematic study of the category GTS of generalized topological spaces (in the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings begins. Some completeness and cocompleteness results are achieved. Generalized topological spaces help to reconstruct the important elements of the theory of locally definable and weakly definable spaces in the wide context of weakly topological structures.
Kuiper, T. B. H.; Resch, G. M.
2000-01-01
The increasing load on NASA's deep Space Network, the new capabilities for deep space missions inherent in a next-generation radio telescope, and the potential of new telescope technology for reducing construction and operation costs suggest a natural marriage between radio astronomy and deep space telecommunications in developing advanced radio telescope concepts.
2006-01-01
The Space Systems Academic Group (SSAG) along with eight academic departments is an integral part of the Graduate School of Engineering and Applied Sciences. As an interdisciplinary association of professors it provides direction and guidance for two curricula: Space Systems Engineering and Space Systems Operations.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Ground has been broken for a new space launch complex in Hainan Province china on September 14 began building a space launch center on tropical Hainan Island and continued to construct the foundations for the nation’s sophisticated space program.
Edwards, William F.; Shiflett, Ray C.; Shultz, Harris
2008-01-01
The mathematical model used to describe independence between two events in probability has a non-intuitive consequence called dependent spaces. The paper begins with a very brief history of the development of probability, then defines dependent spaces, and reviews what is known about finite spaces with uniform probability. The study of finite…
Veen, van der Anne; Otter, Henriëtte S.
2002-01-01
Economists have devoted more attention to the scale of time than to the scale of space. What has been done in the field of space is often general and abstract, not connected to an explicit observation set in time and space. Moreover, time scales and spatial scales are not tied, making the choice for
Pick, Luboš; John, Oldrich; Fucík, Svatopluk
2012-01-01
This is the first part of the second revised and extended edition of a well established monograph. It is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces to study other topics such as partial differential equations. Volum
Heckmann, Reinhold
1995-01-01
Valuations are measure-like functions mapping the open sets of a topological space into positive real numbers. They can be classified according to some additional properties. Some topological spaces are defined whose elements are valuations from various classes. The relationships among these spaces are studied, and universal properties are shown for some of them.
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
With the successful launch of Tiangong-1 (Heavenly Palace-1) unmanned module on September 29,China took a significant step forward in realizing its ambitions in space.China’s manned space program consists of three steps.The first step,to send an astronaut into space,was achieved in 2003.The
Allen Schick
2009-01-01
Fiscal space refers to the financial resources available to a government for policy initiatives through the budget and related decisions. This article reviews the factors that contribute to the shrinkage of fiscal space, considers methods for protecting or enlarging it, and reflects on how budgeting may be recast into a process for explicitly allocating scarce fiscal space.
Institute of Scientific and Technical Information of China (English)
Zhong Jin RUAN (Zhong-Jin Ruan)
2003-01-01
During the last ten to fifteen years , a lot of progress has been achieved in the study ofcomplex operator spaces. In this paper, we show that a corresponding theory can be developed forreal operator spaces. With some appropriate modifications, many complex results still hold for realoperator spaces.
International Nuclear Information System (INIS)
As more people spend more time in space, and the return to the moon and exploratory missions are considered, the risks require continuing examination. The effects of microgravity and radiation are two potential risks in space. These risks increase with increasing mission duration. This document considers the risk of radiation effects in space workers and explorers. 17 refs., 1 fig., 4 tabs
Cocchini, Gianna; Watling, Rosamond; Della Sala, Sergio; Jansari, Ashok
2007-01-01
Successful interaction with the environment depends upon our ability to retain and update visuo-spatial information of both front and back egocentric space. Several studies have observed that healthy people tend to show a displacement of the egocentric frame of reference towards the left. However representation of space behind us (back space) has…
Affordable Space Tourism: SpaceStationSim
2006-01-01
For over 5 years, people have been living and working in space on the International Space Station (ISS), a state-of-the-art laboratory complex orbiting high above the Earth. Offering a large, sustained microgravity environment that cannot be duplicated on Earth, the ISS furthers humankind s knowledge of science and how the body functions for extended periods of time in space all of which will prove vital on long-duration missions to Mars. On-orbit construction of the station began in November 1998, with the launch of the Russian Zarya Control Module, which provided battery power and fuel storage. This module was followed by additional components and supplies over the course of several months. In November 2000, the first ISS Expedition crew moved in. Since then, the ISS has continued to change and evolve. The space station is currently 240 feet wide, measured across the solar arrays, and 171 feet long, from the NASA Destiny Laboratory to the Russian Zvezda Habitation Module. It is 90 feet tall, and it weighs approximately 404,000 pounds. Crews inhabit a living space of about 15,000 cubic feet. To date, 90 scientific investigations have been conducted on the space station. New results from space station research, from basic science to exploration research, are being published each month, and more breakthroughs are likely to come. It is not all work on the space station, though. The orbiting home affords many of the comforts one finds on Earth. There is a weightless "weight room" and even a musical keyboard alongside research facilities. Holidays are observed, and with them, traditional foods such as turkey and cobbler are eaten, with lemonade to wash them down
Recursive space: play and creating space
Wood, Aylish
2012-01-01
Space is reconfigured through the participations of both gamers and the game, where game is understood as the programming and hardware of a game technology. Extending our understandings of the contributions of both gamer and game, the outcome of play emerges as the agencies of each are co-constituted. This space is recursive, based on feedback between the state of the game (relations between the objects) and the state of the gamer, which includes their knowledge, skill, mood and attention. Th...
Directory of Open Access Journals (Sweden)
Jain Rupali S.
2014-12-01
Full Text Available In the present paper, we investigate the qualitative properties such as existence, uniqueness and continuous dependence on initial data of mild solutions of first and second order nonlocal semilinear functional differential equations with delay in Banach spaces. Our analysis is based on semigroup theory and modified version of Banach contraction theorem.
1990-02-01
An overview of the mission of the Hubble Space Telescope, a joint project between NASA and the European Space Agency which will be used to study deep space, as well as our solar system is presented. The video contains animations depicting the Hubble Space Telescope in orbit, as well as footage of scientists at the Space Telescope Science Institute making real time observations. The images Hubble acquires will be downloaded into a database that contains images of over 19,000,0000 celestial objects called the Star Catalog.
U.S. Geological Survey
2008-01-01
Interested in a photograph of the first space walk by an American astronaut, or the first photograph from space of a solar eclipse? Or maybe your interest is in a specific geologic, oceanic, or meteorological phenomenon? The U.S. Geological Survey (USGS) Earth Resources Observation and Science (EROS) Center is making photographs of the Earth taken from space available for search, download, and ordering. These photographs were taken by Gemini mission astronauts with handheld cameras or by the Large Format Camera that flew on space shuttle Challenger in October 1984. Space photographs are distributed by EROS only as high-resolution scanned or medium-resolution digital products.
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
China’s manned space station ambitions take shape with the launch of a prototype module CHINA’S first unmanned space module Tiangong-1,or Heavenly Palace-1,successfully lifted off from the Jiuquan Satellite Launch Center in northwest China’s Gansu Province on September 29."The successful launch of the 8.5-ton prototype space laboratory has opened the gates for China’s deep space exploration program,"said Qi Faren,former chief designer of China’s Shenzhou space-
Energy Technology Data Exchange (ETDEWEB)
WILLIS WL; AHRENDT MR
2009-08-11
Since this report was originally issued in 2001, several options proposed for increasing double-shell tank (DST) storage space were implemented or are in the process of implementation. Changes to the single-shell tank (SST) waste retrieval schedule, completion of DST space saving options, and the DST space saving options in progress have delayed the projected shortfall of DST storage space from the 2007-2011 to the 2018-2025 timeframe (ORP-11242, River Protection Project System Plan). This report reevaluates options from Rev. 0 and includes evaluations of new options for alleviating projected restrictions on SST waste retrieval beginning in 2018 because of the lack of DST storage space.
Tischler, A. O.
1973-01-01
It is pointed out that a contradiction between boundless space and limited resources has put the space program in the distressing position of cutting good and worthy projects from its activities during this decade. One approach to ameliorate the situation is to increase the productivity of space activities by greater utilization of the equipment developed for its projects. The Space Shuttle constitutes the first big step in that direction. The reusable character of the Shuttle orbiter will cut operational costs by permitting recovery and reuse of payload equipment through routine round-trip operations to space.
International Nuclear Information System (INIS)
Since this report was originally issued in 2001, several options proposed for increasing double-shell tank (DST) storage space were implemented or are in the process of implementation. Changes to the single-shell tank (SST) waste retrieval schedule, completion of DST space saving options, and the DST space saving options in progress have delayed the projected shortfall of DST storage space from the 2007-2011 to the 2018-2025 timeframe (ORP-11242, River Protection Project System Plan). This report reevaluates options from Rev. 0 and includes evaluations of new options for alleviating projected restrictions on SST waste retrieval beginning in 2018 because of the lack of DST storage space.
Optimization Research of Urban Space Configuration Based on Space Syntax
Institute of Scientific and Technical Information of China (English)
Zhu Qing; Wang Jingwen
2005-01-01
In this paper, a new method based on the space syntax is presented to optimize the urban space configuration. Space syntax theory is used to detect systematically whether one urban space configuration is optimal or not from four aspects including traffic space, cognition space, land use space and culture space. After introducing the computational and cognitive aspects of space syntax for the research of urban space, a framework of urban space optimization based on space syntax is proposed, then the integration with GIS and the extension to third dimension are discussed. Finally, a case study for Kanmen town of Zhejiang province of P.R.China is illustrated by using Axwoman tool.
Injective Spaces via Adjunction
Hofmann, Dirk
2008-01-01
Our work over the past years shows that not only the collection of (for instance) all topological spaces gives rise to a category, but also each topological space can be seen individually as a category by interpreting the convergence relation $\\mathfrak{x}\\to x$ between ultrafilters and points of a topological space $X$ as arrows in $X$. Naturally, this point of view opens the door to the use of concepts and ideas from (enriched) Category Theory for the investigation of (for instance) topological spaces. In this paper we study cocompleteness, adjoint functors and Kan extensions in the context of topological theories. We show that the cocomplete spaces are precisely the injective spaces, and they are algebras for a suitable monad on $\\SET$. This way we obtain enriched versions of known results about injective topological spaces and continuous lattices.
Freidel, Laurent; Minic, Djordje
2016-01-01
At present, our notion of space is a classical concept. Taking the point of view that quantum theory is more fundamental than classical physics, and that space should be given a purely quantum definition, we revisit the notion of Euclidean space from the point of view of quantum mechanics. Since space appears in physics in the form of labels on relativistic fields or Schrodinger wave functionals, we propose to define Euclidean quantum space as a choice of polarization for the Heisenberg algebra of quantum theory. We show, following Mackey, that generically, such polarizations contain a fundamental length scale and that contrary to what is implied by the Schrodinger polarization, they possess topologically distinct spectra. These are the modular spaces. We show that they naturally come equipped with additional geometrical structures usually encountered in the context of string theory or generalized geometry. Moreover, we show how modular space reconciles the presence of a fundamental scale with translation and...
Space Qualified Heterogeneous Processing Project
National Aeronautics and Space Administration — Space Micro proposes to develop a radiation hardened, monolithic, heterogeneous processor for space imaging and radar systems. High performance processors are...
Space Technology Research Grants Program
National Aeronautics and Space Administration — The Space Technology Research Grants Program will accelerate the development of "push" technologies to support the future space science and exploration...
Kihn, E. A.; Ridley, A. J.; Zhizhin, M.
2002-12-01
The objective of this project is to generate a complete 11 year space weather representation using physically consistent data-driven space weather models. The project will create a consistent, integrated historical record of the near Earth space environment by coupling observational data from space environmental monitoring systems archived at NGDC with data-driven, physically based numerical models. The resulting product will be an enhanced look at the space environment on consistent grids, time resolution, coordinate systems and containing key fields allowing an interested user to quickly and easily incorporate the impact of the near-Earth space climate in environmentally sensitive models. Currently there are no easily accessible long term climate archives available for the space-weather environment. Just as with terrestrial weather it is crucial to understand both daily weather forecasts as well as long term climate changes, so this project will demonstrate the ability to generate a meaningful and physically derived space weather climatology. The results of this project strongly support the DOD's Environmental Scenario Generator (ESG) project. The ESG project provides tools for intellegent data mining, classification and event detection which could be applied to a historical space-weather database. The two projects together provide a suite of tools for the user interested in modeling the effect of the near-earth space environment. We will present results and methodologies developed during the first two years of effort in the project.
INFORMATION SPACE– EDUCATIONAL SPACE
Directory of Open Access Journals (Sweden)
Monica LIA
2015-11-01
Full Text Available This paper has set the objective of researching how education is influenced by the information society. The first step was to define more precisely the information space. The second step was to identify how information space intersects with the family space and institutional space educational levels represented by pre-school / school and pre-university (kindergarten, at elementary / middle school / high school. Interrelationship between the above mentioned areas was another objective of the research. All these elements have been investigated through the original intention to identify how the information space can become an educational tool to support the family space, education and institutional space. Also, the aim of this research is to offer some solutions in this regard. Often the educational efforts appear to be blocked by the existence of this space. But this paper demonstrates that Informational space can be an enemy of the educational system or can support systems if we knew the internal structure and mechanisms. We can make the Informational Space to work in order to accomplish the educational scope.
Space magnetometry. From the Earth into space
International Nuclear Information System (INIS)
Complete text of publication follows. The development of rocket technology made magnetic field measurements above the Earth's atmosphere possible. Measurements in space also depended on the availability of instrumentation capable of surviving the launch and space environments and the duration of the measurements was greatly extended by the development of solar cells to provide power. By good fortune and as a result of having just graduated with a university degree in physics, I became involved in some of the earliest experiments to study the magnetic fields in space. How little we knew and how much to discover. Experience gained on sub-orbital rocket flights led to magnetometers on many of the early spacecraft. While NASA was just getting under way, the USAF Space Technology Laboratories, where I worked initially, launched Explorer 6 into the magnetosphere where it detected the field of the ring current and established the existence of the magnetotail. Pioneer 5 became the first deep space probe and provided the first observations of the interplanetary magnetic field. As the NASA programs took over, I moved to JPL, the designated center for missions to other planets and participated in Mariners 2 and 5 to Venus and Mariner 4 to Mars. I also pursued other opportunities on missions managed by Goddard Space Flight Center (Orbiting Geophysical Observatories 1-6, International Sun- Earth Explorer 3/ International Cometary Explorer) and Ames Research Center (Pioneer 10 to Jupiter and Pioneer 11 to Jupiter and Saturn). Every history, no matter how long and widespread it may become, has a beginning. This talk will describe these early magnetospheric and planetary missions, their magnetic field instrumentation and their principal scientific achievements.
VARIOUS COLOUR SPACES AND COLOUR SPACE CONVERSION
Nishad PM
2013-01-01
A color model is an abstract mathematical model describing the way colors can be represented as tuples of numbers, typically as three or four values or color components (e.g. RGB and CMYK are color models). However, a color model with no associated mapping function to an absolute color space is a more or less arbitrary color system with no connection to any globally understood system of color interpretation. This paper mainly discusses about various colour spaces and the how they organized an...
Ignatiev, A.
2000-01-01
Contents include following: Developing Technologies for Space Resource Utilization - Concept for a Planetary Engineering Research Institute. Results of a Conceptual Systems Analysis of Systems for 200 m Deep Sampling of the Martian Subsurface. The Role of Near-Earth Asteroids in Long-Term Platinum Supply. Core Drilling for Extra-Terrestrial Mining. Recommendations by the "LSP and Manufacturing" Group to the NSF-NASA Workshop on Autonomous Construction and Manufacturing for Space Electrical Power Systems. Plasma Processing of Lunar and Planetary Materials. Percussive Force Magnitude in Permafrost. Summary of the Issues Regarding the Martian Subsurface Explorer. A Costing Strategy for Manufacturing in Orbit Using Extraterrestrial Resources. Mine Planning for Asteroid Orebodies. Organic-based Dissolution of Silicates: A New Approach to Element Extraction from LunarRegohth. Historic Frontier Processes Active in Future Space-based Mineral Extraction. The Near-Earth Space Surveillance (NIESS) Mission: Discovery, Tracking, and Characterization of Asteroids, Comets, and Artificial Satellites with a microsatellite. Privatized Space Resource Property Ownership. The Fabrication of Silicon Solar Cells on the Moon Using In-Situ Resources. A New Strategy for Exploration Technology Development: The Human Exploration and Development of Space (HEDS) Exploratiori/Commercialization Technology Initiative. Space Resources for Space Tourism. Recovery of Volatiles from the Moon and Associated Issues. Preliminary Analysis of a Small Robot for Martian Regolith Excavation. The Registration of Space-based Property. Continuous Processing with Mars Gases. Drilling and Logging in Space; An Oil-Well Perspective. LORPEX for Power Surges: Drilling, Rock Crushing. An End-To-End Near-Earth Asteroid Resource Exploitation Plan. An Engineering and Cost Model for Human Space Settlement Architectures: Focus on Space Hotels and Moon/Mars Exploration. The Development and Realization of a Silicon-60-based
Space-QUEST: Experiments with quantum entanglement in space
2008-01-01
The European Space Agency (ESA) has supported a range of studies in the field of quantum physics and quantum information science in space for several years, and consequently we have submitted the mission proposal Space-QUEST (Quantum Entanglement for Space Experiments) to the European Life and Physical Sciences in Space Program. We propose to perform space-to-ground quantum communication tests from the International Space Station (ISS). We present the proposed experiments in space as well as ...