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Fundamentals of Functional Analysis

  • Book
  • © 1996

Overview

Authors:
  1. S. S. Kutateladze

    1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

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Part of the book series: Texts in the Mathematical Sciences (TMS, volume 12)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xiv
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  2. An Excursion into Set Theory

    • S. S. Kutateladze
    Pages 1-9

  3. Vector Spaces

    • S. S. Kutateladze
    Pages 10-19

  4. Convex Analysis

    • S. S. Kutateladze
    Pages 20-39

  5. An Excursion into Metric Spaces

    • S. S. Kutateladze
    Pages 40-55

  6. Multinormed and Banach Spaces

    • S. S. Kutateladze
    Pages 56-79

  7. Hilbert Spaces

    • S. S. Kutateladze
    Pages 80-99

  8. Principles of Banach Spaces

    • S. S. Kutateladze
    Pages 100-119

  9. Operators in Banach Spaces

    • S. S. Kutateladze
    Pages 120-145

  10. An Excursion into General Topology

    • S. S. Kutateladze
    Pages 146-168

  11. Duality and Its Applications

    • S. S. Kutateladze
    Pages 169-212

  12. Banach Algebras

    • S. S. Kutateladze
    Pages 213-235

  13. Back Matter

    Pages 237-277
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Keywords

About this book

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.

Authors and Affiliations

  • Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    S. S. Kutateladze

Bibliographic Information

  • Book Title: Fundamentals of Functional Analysis

  • Authors: S. S. Kutateladze

  • Series Title: Texts in the Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-94-015-8755-6

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media B.V. 1996

  • Hardcover ISBN: 978-0-7923-3898-7Published: 29 February 1996

  • Softcover ISBN: 978-90-481-4661-1Published: 08 December 2010

  • eBook ISBN: 978-94-015-8755-6Published: 09 March 2013

  • Series ISSN: 0927-4529

  • Edition Number: 1

  • Number of Pages: XIV, 278

  • Additional Information: Originally published in Russian

  • Topics: Functional Analysis, Operator Theory

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