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＜電子ブック＞
Fundamentals of Functional Analysis / by Semën Samsonovich Kutateladze
(Texts in the Mathematical Sciences ; 12)

版	1st ed. 1996.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1996
本文言語	英語
大きさ	XIV, 278 p : online resource
著者標目	*Kutateladze, Semën Samsonovich author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Operator theory FREE:Functional Analysis FREE:Operator Theory
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-94-015-8755-6

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