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Fundamentals of Functional Analysis

Author: S S Kutateladze
Publisher: Dordrecht : Springer Netherlands, 1996.
Series: Kluwer Texts in the Mathematical Sciences, A Graduate-Level Book Series, 12.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: S S Kutateladze
ISBN: 9789401587556 9401587558
OCLC Number: 851391470
Description: 1 online resource (xiv, 277 pages).
Contents: 1. 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.
Series Title: Kluwer Texts in the Mathematical Sciences, A Graduate-Level Book Series, 12.
Responsibility: by S.S. Kutateladze.
More information:

Abstract:

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.

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