Topics In Banach Space Theory

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Topics in Banach Space Theory

Fernando Albiac,Nigel J. Kalton
Topics in Banach Space Theory Book PDF

Author : Fernando Albiac,Nigel J. Kalton
Publisher : Springer
Page : 508 pages
File Size : 49,6 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

An Introduction to Banach Space Theory

Robert E. Megginson
An Introduction to Banach Space Theory Book PDF

Author : Robert E. Megginson
Publisher : Springer Science & Business Media
Page : 613 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206033

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An Introduction to Banach Space Theory by Robert E. Megginson Pdf

Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.

Banach Space Theory

Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler
Banach Space Theory Book PDF

Author : Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler
Publisher : Springer Science & Business Media
Page : 820 pages
File Size : 47,8 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.

A Short Course on Banach Space Theory

N. L. Carothers
A Short Course on Banach Space Theory Book PDF

Author : N. L. Carothers
Publisher : Cambridge University Press
Page : 206 pages
File Size : 52,6 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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Three-space Problems in Banach Space Theory

Jesus M.F. Castillo,Manuel González
Three space Problems in Banach Space Theory Book PDF

Author : Jesus M.F. Castillo,Manuel González
Publisher : Springer
Page : 280 pages
File Size : 41,5 Mb
Release : 2007-12-03
Category : Mathematics
ISBN : 9783540695196

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Three-space Problems in Banach Space Theory by Jesus M.F. Castillo,Manuel González Pdf

This book on Banach space theory focuses on what have been called three-space problems. It contains a fairly complete description of ideas, methods, results and counterexamples. It can be considered self-contained, beyond a course in functional analysis and some familiarity with modern Banach space methods. It will be of interest to researchers for its methods and open problems, and to students for the exposition of techniques and examples.

Functional Analysis

Terry J. Morrison
Functional Analysis Book PDF

Author : Terry J. Morrison
Publisher : John Wiley & Sons
Page : 380 pages
File Size : 42,5 Mb
Release : 2011-10-14
Category : Mathematics
ISBN : 9781118031247

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Functional Analysis by Terry J. Morrison Pdf

A powerful introduction to one of the most active areas of theoretical and applied mathematics This distinctive introduction to one of the most far-reaching and beautiful areas of mathematics focuses on Banach spaces as the milieu in which most of the fundamental concepts are presented. While occasionally using the more general topological vector space and locally convex space setting, it emphasizes the development of the reader's mathematical maturity and the ability to both understand and "do" mathematics. In so doing, Functional Analysis provides a strong springboard for further exploration on the wide range of topics the book presents, including: * Weak topologies and applications * Operators on Banach spaces * Bases in Banach spaces * Sequences, series, and geometry in Banach spaces Stressing the general techniques underlying the proofs, Functional Analysis also features many exercises for immediate clarification of points under discussion. This thoughtful, well-organized synthesis of the work of those mathematicians who created the discipline of functional analysis as we know it today also provides a rich source of research topics and reference material.

Banach Spaces for Analysts

P. Wojtaszczyk
Banach Spaces for Analysts Book PDF

Author : P. Wojtaszczyk
Publisher : Cambridge University Press
Page : 400 pages
File Size : 40,5 Mb
Release : 1996-08
Category : Mathematics
ISBN : 0521566754

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Banach Spaces for Analysts by P. Wojtaszczyk Pdf

This book is intended to be used with graduate courses in Banach space theory.

History of Banach Spaces and Linear Operators

Albrecht Pietsch
History of Banach Spaces and Linear Operators Book PDF

Author : Albrecht Pietsch
Publisher : Springer Science & Business Media
Page : 855 pages
File Size : 43,5 Mb
Release : 2007-12-31
Category : Mathematics
ISBN : 9780817645960

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History of Banach Spaces and Linear Operators by Albrecht Pietsch Pdf

Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.

Banach Space Theory

Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler
Banach Space Theory Book PDF

Author : Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler
Publisher : Springer
Page : 822 pages
File Size : 47,5 Mb
Release : 2010-12-15
Category : Mathematics
ISBN : 1441975144

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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.

A Short Course on Banach Space Theory

N. L. Carothers
A Short Course on Banach Space Theory Book PDF

Author : N. L. Carothers
Publisher : Cambridge University Press
Page : 199 pages
File Size : 55,5 Mb
Release : 2005
Category : Mathematics
ISBN : 9780521842839

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

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Biorthogonal Systems in Banach Spaces

Petr Hajek,Vicente Montesinos Santalucia,Jon Vanderwerff,Vaclav Zizler
Biorthogonal Systems in Banach Spaces Book PDF

Author : Petr Hajek,Vicente Montesinos Santalucia,Jon Vanderwerff,Vaclav Zizler
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 51,6 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.

Banach Spaces and Descriptive Set Theory: Selected Topics

Pandelis Dodos
Banach Spaces and Descriptive Set Theory Selected Topics Book PDF

Author : Pandelis Dodos
Publisher : Springer Science & Business Media
Page : 180 pages
File Size : 51,6 Mb
Release : 2010-05-10
Category : Mathematics
ISBN : 9783642121524

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Banach Spaces and Descriptive Set Theory: Selected Topics by Pandelis Dodos Pdf

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.

Topics in Banach Space Integration

?tefan Schwabik,Guoju Ye
Topics in Banach Space Integration Book PDF

Author : ?tefan Schwabik,Guoju Ye
Publisher : World Scientific
Page : 313 pages
File Size : 44,5 Mb
Release : 2005
Category : Mathematics
ISBN : 9789812564283

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Topics in Banach Space Integration by ?tefan Schwabik,Guoju Ye Pdf

The relatively new concepts of the Henstock-Kurzweil and McShane integrals based on Riemann type sums are an interesting challenge in the study of integration of Banach space-valued functions. This timely book presents an overview of the concepts developed and results achieved during the past 15 years. The Henstock-Kurzweil and McShane integrals play the central role in the book. Various forms of the integration are introduced and compared from the viewpoint of their generality. Functional analysis is the main tool for presenting the theory of summation gauge integrals.

Probability in Banach Spaces

Michel Ledoux,Michel Talagrand
Probability in Banach Spaces Book PDF

Author : Michel Ledoux,Michel Talagrand
Publisher : Springer Science & Business Media
Page : 493 pages
File Size : 54,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783642202124

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Probability in Banach Spaces by Michel Ledoux,Michel Talagrand Pdf

Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.

Methods in Banach Space Theory

Jesus M. F. Castillo,William B. Johnson
Methods in Banach Space Theory Book PDF

Author : Jesus M. F. Castillo,William B. Johnson
Publisher : Cambridge University Press
Page : 371 pages
File Size : 51,5 Mb
Release : 2006-11-30
Category : Mathematics
ISBN : 9780521685689

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Methods in Banach Space Theory by Jesus M. F. Castillo,William B. Johnson Pdf

A comprehensive overview of modern Banach space theory.