Fundamentals of Functional Analysis (Paperback)

Semen Samsonovich Kutateladze

ISBN 10: 9048146615 / ISBN 13: 9789048146611

Editore: Springer, Dordrecht, 2010

Paperback. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9789048146611

Riassunto:

to the English Translation 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. With standard provisos the presentation is self-contained, exposing about a h- dred famous "named" theorems furnished with complete proofs and culminating in the Gelfand-Nalmark-Segal construction for C*-algebras. The first Russian edition was printed by the Siberian Division of "Nauka" P- lishers in 1983. Since then the monograph has served as the standard textbook on functional analysis at the University of Novosibirsk. This volume is translated from the second Russian edition printed by the Sobolev Institute of Mathematics of the Siberian Division of the Russian Academy of Sciences· in 1995. It incorporates new sections on Radon measures, the Schwartz spaces of distributions, and a supplementary list of theoretical exercises and problems. This edition was typeset using AMS-'lEX, the American Mathematical Society's 'lEX system. To clear my conscience completely, I also confess that := stands for the definor, the assignment operator, signifies the end of the proof.

Contenuti: 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. Subject Index.

Dati bibliografici

Titolo: Fundamentals of Functional Analysis (...
Casa editrice: Springer, Dordrecht
Data di pubblicazione: 2010
Legatura: Paperback
Condizione: new
Edizione: prima edizione