\(\phi\)-amenability and character amenability of some classes of Banach algebras
type: Item
instance of: scholarly article
zbMATH Open document ID: 1275.43004
author: M. Essmaili
author: M. Filali
publication date: 2013-07-15T00:00:00Z
Mathematics Subject Classification ID: 43A20
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 16E40
zbMATH DE Number: 6188003
zbMATH Keywords: Banach algebra
zbMATH Keywords: semigroup algebra
zbMATH Keywords: \(\phi\)-amenability
zbMATH Keywords: character amenability
MaRDI profile type: Publication
title: \(\phi\)-amenability and character amenability of some classes of Banach algebras
published in: Houston Journal of Mathematics
review text: Let \(A\) be a Banach algebra, and let \(\phi\) be a character (i.e., non-zero multiplicative linear functional) on \(A\). Then \(A\) is said to be \(\phi\)-amenable if, for every Banach \(A\)-bimodule \(X\) such that \(a\cdot x=\phi(a)x\) for all \(a\in A\) and \(x\in X\), each continuous derivation from \(A\) into the dual \(X^*\) is inner. The authors call \(A\) character amenable if \(A\) is \(\phi\)-amenable for each character \(\phi\) and \(A\) has a bounded right approximate identity. The authors study the above introduced notions for the semigroup algebra \(\ell^1(S)\) corresponding to a semilattice \(S\). Further, they characterize the character amenability of \(\ell^1(S)\) in the case where \(S\) is a uniformly locally finite inverse semigroup.
reviewed by: Armando R. Villena
description: scientific article; zbMATH DE number 6188003