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Amenable locally compact groups. (English) Zbl 0621.43001
Pure and Applied Mathematics. A Wiley-Interscience Publication. New York etc.: John Wiley & Sons. X, 418 p. £49.80 (1984).

This book is a comprehensive monograph on the theory of amenable locally compact groups. The prerequisites for reading this are collected in the first chapter. Chapter 2 gives various fundamental characterizations of amenable locally compact groups, e.g., the common fixed point properties, the Day’s asymptotical invariance properties, the Reiter’s conditions, the Glicksberg-Reiter property, the Følner’s conditions, the weak containment property, the cohomological characterizations and so forth.

Chapter 3 gives examples of amenable groups and studies the class of amenable groups. Chapters 4 and 5 give further details on necessary and/or sufficient conditions for locally compact groups to be amenable. The final chapter gives some supplementary description of the class of amenable groups and briefly indicates various directions into which amenability properties have been generalized.

This book may facilitate further studies on the phenomenon of amenability, and the notes at the end of some sections and the bibliography may provide meaningful informations on the theory of amenability for us.

[This review replaces the one in Zbl 0597.43001.]

Reviewer: K.Sakai

MSC:
43-02Research monographs (abstract harmonic analysis)
22-02Research monographs (topological groups)
43A07Means on groups, semigroups, etc.; amenable groups
22D05General properties and structure of locally compact groups