Topics in Banach Space Theory

Topics in Banach Space Theory
Author: Fernando Albiac
Publisher: Springer
Total Pages: 512
Release: 2016-07-19
Genre: Mathematics
ISBN: 3319315579

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

Banach Space Theory

Banach Space Theory
Author: Marián Fabian
Publisher: Springer Science & Business Media
Total Pages: 820
Release: 2011-02-04
Genre: Mathematics
ISBN: 1441975152

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.

An Introduction to Banach Space Theory

An Introduction to Banach Space Theory
Author: Robert E. Megginson
Publisher: Springer Science & Business Media
Total Pages: 613
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461206030

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.

Functional Analysis

Functional Analysis
Author: Terry J. Morrison
Publisher: John Wiley & Sons
Total Pages: 380
Release: 2011-10-14
Genre: Mathematics
ISBN: 1118031245

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

Banach Spaces for Analysts
Author: P. Wojtaszczyk
Publisher: Cambridge University Press
Total Pages: 400
Release: 1996-08
Genre: Mathematics
ISBN: 9780521566759

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

Three-space Problems in Banach Space Theory

Three-space Problems in Banach Space Theory
Author: Jesus M.F. Castillo
Publisher: Springer
Total Pages: 280
Release: 2007-12-03
Genre: Mathematics
ISBN: 3540695192

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.

Banach Spaces and Descriptive Set Theory: Selected Topics

Banach Spaces and Descriptive Set Theory: Selected Topics
Author: Pandelis Dodos
Publisher: Springer Science & Business Media
Total Pages: 180
Release: 2010-05-10
Genre: Mathematics
ISBN: 3642121527

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.

Methods in Banach Space Theory

Methods in Banach Space Theory
Author: Jesus M. F. Castillo
Publisher: Cambridge University Press
Total Pages: 371
Release: 2006-11-30
Genre: Mathematics
ISBN: 0521685680

A comprehensive overview of modern Banach space theory.