Lectures on Amenability

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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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.

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

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