Amenable Locally Compact GroupsCollects 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. |
Contents
Preliminaries | 1 |
Processes | 23 |
Fundamental Characterizations of Amenable Groups | 30 |
Copyright | |
7 other sections not shown
Common terms and phrases
a₁ abelian group amenable group Amer approximate units Banach A-module Banach algebra Banach space bounded C*-algebra closed subgroup closed under complex co² compact neighborhood compact subset consider convex Corollary defined discrete group element equivalent ergodic exists a compact F₁ F₂ finite subset fixed point following properties G is amenable Granirer group and let group G Haar measure hence hermitian homomorphism implies K₁ L¹(G L³(G left invariant mean Lemma Let G Lie group locally compact group LP(G LR(G M₁ M¹(G mapping Math measurable subset nonamenable noncompact nonvoid normal subgroup P₁ P¹(G PM(G positive-definite probability measure Proof Proposition representation resp right invariant RUC(G semigroups semisimple sequence subgroup H subgroup of G subset of G subspace Theorem TLIM topological group topologically left invariant U₁ UC(G unimodular V₁ von Neumann algebra µ Є