Bases In Banach Spaces

Author : Christopher Heil
Publisher : Springer Science & Business Media
Page : 549 pages
File Size : 52,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9780817646868

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A Basis Theory Primer by Christopher Heil Pdf

This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses. The self-contained presentation with clear proofs is accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications.

Author : Z. Semadeni
Publisher : Springer
Page : 142 pages
File Size : 53,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540391432

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Schauder Bases in Banach Spaces of Continuous Functions by Z. Semadeni Pdf

Author : Ivan Singer
Publisher : Springer
Page : 688 pages
File Size : 52,8 Mb
Release : 1970
Category : Mathematics
ISBN : UOM:39015015690558

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Bases in Banach Spaces by Ivan Singer Pdf

Author : Ivan Singer
Publisher : Springer
Page : 688 pages
File Size : 42,8 Mb
Release : 1970
Category : Mathematics
ISBN : UOM:39015015690541

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Bases in Banach Spaces by Ivan Singer Pdf

Author : Ivan Singer
Publisher : Springer
Page : 902 pages
File Size : 44,7 Mb
Release : 1970
Category : Mathematics
ISBN : PSU:000006320867

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Bases in Banach Spaces by Ivan Singer Pdf

Author : Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler
Publisher : Springer Science & Business Media
Page : 820 pages
File Size : 40,9 Mb
Release : 2011-02-04
Category : Mathematics
ISBN : 9781441975157

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Banach Space Theory by Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler Pdf

Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.

Author : J. Lindenstrauss,L. Tzafriri
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 45,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783642665578

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Classical Banach Spaces I by J. Lindenstrauss,L. Tzafriri Pdf

The appearance of Banach's book [8] in 1932 signified the beginning of a syste matic study of normed linear spaces, which have been the subject of continuous research ever since. In the sixties, and especially in the last decade, the research activity in this area grew considerably. As a result, Ban:ach space theory gained very much in depth as well as in scope: Most of its well known classical problems were solved, many interesting new directions were developed, and deep connections between Banach space theory and other areas of mathematics were established. The purpose of this book is to present the main results and current research directions in the geometry of Banach spaces, with an emphasis on the study of the structure of the classical Banach spaces, that is C(K) and Lip.) and related spaces. We did not attempt to write a comprehensive survey of Banach space theory, or even only of the theory of classical Banach spaces, since the amount of interesting results on the subject makes such a survey practically impossible.

Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 51,5 Mb
Release : 1970
Category : Electronic
ISBN : OCLC:487252300

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Bases in Banach spaces by Anonim Pdf

Author : Jean Bourgain
Publisher : American Mathematical Soc.
Page : 111 pages
File Size : 52,9 Mb
Release : 1985
Category : Banach spaces
ISBN : 9780821823231

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Banach Spaces with a Unique Unconditional Basis, up to Permutation by Jean Bourgain Pdf

Author : Aref Jeribi
Publisher : Walter de Gruyter GmbH & Co KG
Page : 421 pages
File Size : 46,7 Mb
Release : 2018-03-19
Category : Mathematics
ISBN : 9783110493863

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Denseness, Bases and Frames in Banach Spaces and Applications by Aref Jeribi Pdf

This book is devoted to recent developments concerning linear operators, covering topics such as the Cauchy problem, Riesz basis, frames, spectral theory and applications to the Gribov operator in Bargmann space. Also, integral and integro-differential equations as well as applications to problems in mathematical physics and mechanics are discussed. Contents Introduction Linear operators Basic notations and results Bases Semi-groups Discrete operator and denseness of the generalized eigenvectors Frames in Hilbert spaces Summability of series ν-convergence operators Γ-hypercyclic set of linear operators Analytic operators in Béla Szökefalvi-Nagy’s sense Bases of the perturbed operator T(ε) Frame of the perturbed operator T(ε) Perturbation method for sound radiation by a vibrating plate in a light fluid Applications to mathematical models Reggeon field theory

Author : Jürg T. Marti
Publisher : Springer Science & Business Media
Page : 160 pages
File Size : 51,8 Mb
Release : 2013-03-13
Category : Mathematics
ISBN : 9783642871405

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Introduction to the Theory of Bases by Jürg T. Marti Pdf

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

Author : Fernando Albiac,Nigel J. Kalton
Publisher : Springer
Page : 508 pages
File Size : 42,9 Mb
Release : 2016-07-19
Category : Mathematics
ISBN : 9783319315577

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Topics in Banach Space Theory by Fernando Albiac,Nigel J. Kalton Pdf

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 functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. From the reviews of the First Edition: "The authors of the book...succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly... It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments... I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book..."—Gilles Godefroy, Mathematical Reviews

Author : Petr Hajek,Vicente Montesinos Santalucia,Jon Vanderwerff,Vaclav Zizler
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 55,6 Mb
Release : 2007-10-04
Category : Mathematics
ISBN : 9780387689159

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Biorthogonal Systems in Banach Spaces by Petr Hajek,Vicente Montesinos Santalucia,Jon Vanderwerff,Vaclav Zizler Pdf

This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory. The authors have included numerous exercises, as well as open problems that point to possible directions of research.

Author : N. L. Carothers
Publisher : Cambridge University Press
Page : 206 pages
File Size : 45,9 Mb
Release : 2005
Category : Mathematics
ISBN : 0521603722

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A Short Course on Banach Space Theory by N. L. Carothers Pdf

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Author : Ivan Singer
Publisher : Springer
Page : 0 pages
File Size : 48,7 Mb
Release : 2013-09-14
Category : Mathematics
ISBN : 3642516335

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Bases in Banach Spaces I by Ivan Singer Pdf

This monograph attempts to present the results known today on bases in Banach spaces and some unsolved problems concerning them. Although this important part of the theory of Banach spaces has been studied for more than forty years by numerous mathematicians, the existing books on functional analysis (e. g. M. M. Day [43], A. Wilansky [263], R. E. Edwards [54]) contain only a few results on bases. A survey of the theory of bases in Banach spaces, up to 1963, has been presented in the expository papers [241], [242] and [243], which contain no proofs; although in the meantime the theory has rapidly deve1oped, much of the present monograph is based on those expository papers. Independently, a useful bibliography of papers on bases, up to 1963, was compiled by B. L. Sanders [219J. Due to the vastness of the field, the monograph is divided into two volumes, ofwhich this is the first (see the tab1e of contents). Some results and problems re1ated to those treated herein have been de1iberately planned to be inc1uded in Volume 11, where they will appear in their natural framework (see [242], [243]).