zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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

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