Amenable locally compact groups
Collects the most recent results scattered throughout the literature on the theory of amenable groups, presenting a detailed investigation of the major features. The first part of the book discusses the different types of amenability properties, with basic examples listed. The second part provides complementary information on various aspects of amenability and a look at future directions.
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Methods of Modern Mathematical Physics: Functional analysis, Volume 1
Michael Reed,Barry Simon
Limited preview - 1980
Fundamental Characterizations of Amenable Groups
The Class of Amenable Groups
6 other sections not shown
a e G abelian group amenable group Amer Ap(G approximate units Banach algebra Banach G-module Banach space bounded C*-algebra closed subgroup closed under complex compact neighborhood compact subset complex conjugation consider converges convex Corollary defined denote discrete group element equivalent ergodic exists a compact finite subset fixed point following properties Fourier algebra functions G is amenable group and let group G Haar measure hence hermitian Hilbert space homomorphism implies isometries Jf(G left invariant mean Lemma Leptin Let G Lie group linear Ll(G locally compact group LP(G Lr(G mapping Math measurable subset nonamenable noncompact nonvoid normal subgroup Pl(G PM(G positive-definite probability measure Proof resp right invariant Section semisimple sequence subgroup H subgroup of G subset of G subspace of L°°(G Theorem topological group topologically left invariant unimodular x e G