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Mathematics - Analysis | Functional Analysis and Infinite-Dimensional Geometry

Functional Analysis and Infinite-Dimensional Geometry

Fabian, M., Habala, P., Hajek, P., Montesinos Santalucia, V., Pelant, J., Zizler, V.

2001, IX, 451 p.

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Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization, and other branches ofmathematics. This book is intended as an introduction to linear functional analysis and to some parts of infinite-dimensional Banach space theory. The first seven chapters are directed mainly to undergraduate and grad­ uate students. We have strived to make the text easily readable and as self-contained as possible. In particular, we proved many basic facts that are considered "folklore." An important part of the text is a large number of exercises with detailed hints for their solution. They complement the material in the chapters and contain many important results. The last fivechapters introduce the reader to selected topics in the theory of Banach spaces related to smoothness and topology.This part of the book isintended as an introduction to and a complement ofexisting books on the subject ([Bea], [BeLi], [DGZ3]' [Disl], [Dis2], [Fab], [JoL3], [LiT2], [Phe2]' [Woj]). Some material is presented here for the first time in a monograph form. For further reading in this area, we recommend for instance [Gil], [God4], [Gue], [JoL3], [Kec], [LjSo], [Neg], [MeNe]' [Oxt], [RoJa], [Sem], [Sin3], [TaI2], and [Yael. The text is based on graduate courses taught at the University ofAlberta in Edmonton in the years 1984-1997. These courses were also taken by many senior students in the Honors undergraduate program in Edmonton.

Content Level » Graduate

Keywords » Banach Space - Compact operator - Convexity - Operator theory - Smooth function - calculus - compactness - functional analysis

Related subjects » Analysis

Table of contents 

Preface * 1 Basic Concepts in Banach Spaces * 2 Hahn-Banach and Banach Open Mapping Theorems * 3 Weak Topologies * 4 Locally Convex Spaces * 5 Structure of Banach Spaces * 6 Schauder Bases * 7 Compact Operators on Banach Spaces * 8 Differentiability of Norms * 9 Uniform Convexity * 10 Smoothness and Structure * 11 Weakly Compactly Generated Spaces * 12 Topics in Weak Toplogy * References * Index

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