Functional analysis and infinite-dimensional geometry

  • Nombre de pages : 452 pages   drapeau anglais
  • Date de parution : 01/05/2001

Résumé

This book introduces the reader to the basic principles of functional analysis and to areas of Banach space theory that are close to nonlinear analysis and toplogy.

In the first part, the book develops the classical theory, including weak topologies, locally convex spaces, Schauder bases, and compact operator theory. The presentation is self-contained, including many folklore results, and the proofs are accessible to students with the usual background in real analysis and topology. The second part covers topics in convexity and smoothness, finite representability, variational principles, homeomorphisms, weak compactness, and more. Several results are published here for the first time in a monograph. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints. The book is also directed to young researchers in functional analysis and can serve as a reference book.

Table of Contents

Preface
1 Basic Concepts in Banach Spaces 1
2 Hahn-Banach and Banach Open Mapping Theorems 37
3 Weak Topologies 63
4 Locally Convex Spaces 107
5 Structure of Banach Spaces 137
6 Schauder Bases 161
7 Compact Operators on Banach Spaces 203
8 Differentiability of Norms 241
9 Uniform Convexity 285
10 Smoothness and Structure 313
11 Weakly Compactly Generated Spaces 357
12 Topics in Weak Topology 387
References 431
Index 445

Caractéristiques

  • Parution : 01/05/2001
  • Edition : 1ère édition
  •  
  • Nb de pages : 452 pages
  • Format : 16 x 24,3
  • Couverture : Relié
  • Poids : 817 g
  • Intérieur : Noir et Blanc
  •  

Nos clients ont aussi acheté

mentions légales | conditions générales de vente | copyright © 2012
(1) livraison gratuite à partir de 49 € en France métropolitaine