Introduction to Banach Spaces And Their Geometry

Bernard Beauzamy (Eds.)0444864164, 9780444864161

Since the first edition of this well-known text was published in 1982, significant progress has been made in the local theory of Banach Spaces. This second edition has therefore been brought up to date by the addition of a completely new section devoted to this topic, as well as various other revisions, an expanded bibliography and a new appendix.

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Table of contents :
Content:
Edited by
Page iii

Copyright page
Page iv

Introduction
Pages v-viii

Chapter 0 Notations and Preliminaries
Pages 1-4

Chapter I Baire’s Property and its Consequences
Pages 7-16

Chapter II Infinite-Dimensional Normed Spaces
Pages 17-48

Chapter III Reflexive Banach Spaces; Separable Banach Spaces
Pages 49-65

Chapter I Hilbert Spaces
Pages 69-78

Chapter II Schauder Bases in Banach Spaces
Pages 79-98

Chapter III Complemented Subspaces in Banach Spaces
Pages 99-106

Chapter IV The Banach Spaces lp(1 ≤ p ≤ + ∞) and c0
Pages 107-122

Chapter V Extreme Points of Compact Convex Sets and the Banach Spaces (K)
Pages 123-135

Chapter VI the Banach Spaces Lp (Ω, , μ), 1 ≤ p < + ∞
Pages 137-172

Part 3 Some Metric Properties in Banach Spaces
Pages 173-174

Chapter I Strict Convexity and Smoothness
Pages 175-187

Chapter II Uniform Convexity and Uniform Smoothness
Pages 189-214

Part 4 The Geometry of Super-Reflexive Banach Spaces
Pages 215-216

Chapter I Finite Representability and Super-Properties of Banach Spaces
Pages 217-242

Chapter II Basic Sequences in Super-Reflexive Banach Spaces
Pages 243-254

Chapter III Uniformly Non-Square and J-Convex Banach Spaces
Pages 255-271

Chapter IV Renorming Super-Reflexive Banach Spaces
Pages 273-299

Bibliography
Pages 301-304

Index
Pages 305-308