Characterization of amenable semigroups with a unique invariant mean
type: Item
instance of: scholarly article
title: Characterization of amenable semigroups with a unique invariant mean
zbMATH Open document ID: 0544.43002
author: Koukichi Sakaj
published in: Proceedings of the Japan Academy. Series A
publication date: 1983-01-01T00:00:00Z
review text: An amenable semigroup S has the property that, for any a,\(b\in S\), a\(S\cap bS\) and S\(a\cap Sb\) are non-void, and one can define a congruence \(a\sim b\) if and only if \(as=bs\) and \(ta=tb\) for some s,\(t\in S\). The author's main theorem here states that, for amenable S, the following are equivalent: (1) S has a unique left invariant mean. (2) S contains a finite two-sided ideal which is also a group. (3) S has a unique right invariant mean. (4) S/\(\sim\) is a finite group and ker \(\sim\) has a zero element.
Mathematics Subject Classification ID: 43A07
Mathematics Subject Classification ID: 22A20
zbMATH DE Number: 3865926
zbMATH Keywords: amenable semigroup
zbMATH Keywords: invariant mean
MaRDI profile type: Publication
full work available at URL: pjaa.59.321
OpenAlex ID: W1998911804
cites work: Amenable semigroups
cites work: On amenable semigroups with a finite-dimensional set of invariant means. I, II
cites work: Extremely Amenable Semigroups.
cites work: Topological Semigroups with Invariant Means in the Convex Hull of Multiplicative Means
cites work: Characterization of extremely amenable semigroups with a unique invariant mean
cites work: Q3317538
DOI: 10.3792/PJAA.59.321
description: scientific article; zbMATH DE number 3865926