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Lectures on Amenability

  • Book
  • © 2002

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Authors:
  1. Volker Runde
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1774)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xiii
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  2. 0. Paradoxical decompositions

    • Volker Runde
    Pages 1-15

  3. 1. Amenable, locally compact groups

    • Volker Runde
    Pages 17-36

  4. 2. Amenable Banach algebras

    • Volker Runde
    Pages 37-61

  5. 3. Examples of amenable Banach algebras

    • Volker Runde
    Pages 63-81

  6. 4. Amenability-like properties

    • Volker Runde
    Pages 83-117

  7. 5. Banach homology

    • Volker Runde
    Pages 119-139

  8. 6. C*- and W*-algebras

    • Volker Runde
    Pages 141-190

  9. 7. Operator amenability

    • Volker Runde
    Pages 191-207

  10. 8. Geometry of spaces of homomorphisms

    • Volker Runde
    Pages 209-219

  11. Open problems

    • Volker Runde
    Pages 221-229

  12. A Abstract harmonic analysis

    • Volker Runde
    Pages 231-241

  13. B Tensor products

    • Volker Runde
    Pages 243-254

  14. C Banach space properties

    • Volker Runde
    Pages 255-263

  15. D Operator spaces

    • Volker Runde
    Pages 265-274

  16. List of Symbols

    • Volker Runde
    Pages 275-280

  17. References

    • Volker Runde
    Pages 281-288

  18. Index

    • Volker Runde
    Pages 289-296

  19. Back Matter

    Pages 297-299
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Keywords

About this book

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.

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