Synopses & Reviews
This is a concise guide to basic sections of modern functional analysis. Included are such topics as the principles of Banach and Hilbert spaces, the theory of multinormed and uniform spaces, the Riesz-Dunford holomorphic functional calculus, the Fredholm index theory, convex analysis and duality theory for locally convex spaces. More than one hundred famous `named' theorems, culminating in the Gelfand-Naimark-Segal construction for C*-algebras, are treated, and complete proofs are given. This volume, which is regarded already as a standard textbook in functional analysis, has been translated from the second, completely revised and updated Russian edition. It incorporates new sections on the Schwartz spaces of distributions, Radon measures, and a supplementary list of theoretical exercises and problems. Audience: This monograph will be of value to researchers and students who are interested in functional analysis.
Table of Contents
An Excursion into Set Theory. 2.
Vector Spaces. 3.
Convex Analysis. 4.
An Excursion into Metric Spaces. 5.
Multinormed and Banach Spaces. 6.
Hilbert Spaces. 7.
Principles of Banach Spaces. 8.
Operators in Banach Spaces. 9.
An Excursion into General Topology. 10.
Duality and Its Applications. 11.
Banach Algebras. References. Notation Index. Subject Index.