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Fundamentals of Functional Analysis

  • S. S. Kutateladze

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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. S. S. Kutateladze
    Pages 1-9
  3. S. S. Kutateladze
    Pages 10-19
  4. S. S. Kutateladze
    Pages 20-39
  5. S. S. Kutateladze
    Pages 40-55
  6. S. S. Kutateladze
    Pages 56-79
  7. S. S. Kutateladze
    Pages 80-99
  8. S. S. Kutateladze
    Pages 100-119
  9. S. S. Kutateladze
    Pages 120-145
  10. S. S. Kutateladze
    Pages 146-168
  11. S. S. Kutateladze
    Pages 169-212
  12. S. S. Kutateladze
    Pages 213-235
  13. Back Matter
    Pages 237-277

About this book

Introduction

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.

Keywords

C*-algebra Hilbert space distribution functional analysis index theory

Authors and affiliations

  • S. S. Kutateladze
    • 1
  1. 1.Sobolev Institute of MathematicsSiberian Branch of the Russian Academy of SciencesNovosibirskRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8755-6
  • Copyright Information Springer Science+Business Media B.V. 1996
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4661-1
  • Online ISBN 978-94-015-8755-6
  • Series Print ISSN 0927-4529
  • Buy this book on publisher's site
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