\(\Gamma \)-amenability of locally compact groups
type: Item
instance of: scholarly article
title: \(\Gamma \)-amenability of locally compact groups
zbMATH Open document ID: 1219.43001
author: A. Ghaffari
publication date: 2011-03-02T00:00:00Z
review text: The purpose of this paper is to study the notion of \(\Gamma \)-amenability of a locally compact group \(G\), where \(\Gamma \) is a closed subgroup of \(G\times G\). That notion was introduced by \textit{B. Li} and \textit{J.-P. Pier} in [Adv. Math., Beijing 21, No. 1, 97--112 (1992; Zbl 0763.43002)]. In case \(\Gamma =G\times\{e\}\) or \(\Gamma =\{e\}\times G\), \(\Gamma \)-amenability is amenability in the usual sense, and in case \(\Gamma =\text{diag}(G)\), \(\Gamma \)-amenability is equivalent to inner amenability. In this paper the author establishes various characterizations of \(\Gamma \)-amenable groups extending the well-known Følner's conditions. In the last section the author gives sufficient conditions for inner amenability in case of discrete groups.
reviewed by: Mădălina Buneci
Mathematics Subject Classification ID: 43A07
Mathematics Subject Classification ID: 43A15
zbMATH DE Number: 5859368
zbMATH Keywords: amenable groups
zbMATH Keywords: Banach algebras
zbMATH Keywords: locally compact groups
zbMATH Keywords: \(\Gamma \)-amenable groups
zbMATH Keywords: inner invariant means
zbMATH Keywords: unimodular groups
MaRDI profile type: Publication
full work available at URL: s10114-010-9498-0
OpenAlex ID: W2101774558
cites work: Q4888829
cites work: Q4019889
cites work: Q3729546
cites work: Q3876497
cites work: Inner invariant extensions of Dirac measures on compactly cancellative topological semigroups
cites work: Q3431280
cites work: Inner amenability of foundation semigroup algebras
cites work: A characterization of locally compact inner amenable groups
cites work: Structural properties of inner amenable discrete groups
cites work: Inner Amenable Locally Compact Groups
cites work: Conjugate convolutions and inner invariant means
cites work: \(L^ 1\)-algebras and Segal algebras
cites work: Conjugation-invariant means
cites work: Topological inner invariant means
cites work: Inner amenability of locally compact groups and their algebras
cites work: Q3024460
cites work: Q5723435
cites work: Sur le produit de composition. II
cites work: Faltungen von Borelschen Maßen mit \(L^ p\)-Funktionen auf lokal kompakten Gruppen
cites work: Projections onto invariant subspaces of some Banach algebras
cites work: Structural properties of inner amenable groups
DOI: 10.1007/S10114-010-9498-0
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5859368