Functional analysis and infinite-dimensional geometry

Marian Fabian, Petr Habala, Petr Hajek, Vicente Montesinos Santalucia, Jan Pelant, Vaclav Zizler

452 pages, parution le 01/05/2001

Ajouter à une liste

Indisponible

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 techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Marian Fabian, Petr Habala, Petr Hajek, Vicente Montesinos Santalucia, Jan Pelant, Vaclav Zizler
Parution	01/05/2001
Nb. de pages	452
Format	16 x 24,3
Couverture	Relié
Poids	817g
Intérieur	Noir et Blanc
EAN13	9780387952192
ISBN13	978-0-387-95219-2