Lectures on Amenability

  • Authors
  • Volker┬áRunde

Part of the Lecture Notes in Mathematics book series (LNM, volume 1774)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Volker Runde
    Pages 1-15
  3. Volker Runde
    Pages 17-36
  4. Volker Runde
    Pages 37-61
  5. Volker Runde
    Pages 63-81
  6. Volker Runde
    Pages 83-117
  7. Volker Runde
    Pages 119-139
  8. Volker Runde
    Pages 141-190
  9. Volker Runde
    Pages 191-207
  10. Volker Runde
    Pages 209-219
  11. Volker Runde
    Pages 221-229
  12. Volker Runde
    Pages 231-241
  13. Volker Runde
    Pages 243-254
  14. Volker Runde
    Pages 255-263
  15. Volker Runde
    Pages 265-274
  16. Volker Runde
    Pages 275-280
  17. Volker Runde
    Pages 281-288
  18. Volker Runde
    Pages 289-296
  19. Back Matter
    Pages 297-299

About this book

Introduction

The notion of amenability has its origins in the beginnings of modern measure theory: Does a finitely additive set function exist which is invariant under a certain group action? Since the 1940s, amenability has become an important concept in abstract harmonic analysis (or rather, more generally, in the theory of semitopological semigroups). In 1972, B.E. Johnson showed that the amenability of a locally compact group G can be characterized in terms of the Hochschild cohomology of its group algebra L^1(G): this initiated the theory of amenable Banach algebras. Since then, amenability has penetrated other branches of mathematics, such as von Neumann algebras, operator spaces, and even differential geometry. Lectures on Amenability introduces second year graduate students to this fascinating area of modern mathematics and leads them to a level from where they can go on to read original papers on the subject. Numerous exercises are interspersed in the text.

Keywords

Algebra Cohomology amenable Banach algebras amenable and locally compact groups amenable von Neumann algebras harmonic analysis homomorphism operator amenability

Bibliographic information

  • DOI https://doi.org/10.1007/b82937
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-42852-7
  • Online ISBN 978-3-540-45560-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book