Pseudo-amenability of certain semigroup algebras
type: Item
instance of: scholarly article
title: Pseudo-amenability of certain semigroup algebras
zbMATH Open document ID: 1223.43001
published in: Semigroup Forum
publication date: 2011-09-06T00:00:00Z
review text: Let \(S\) be an inverse semigroup with uniformly locally finite idempotent set. \textit{F. Ghahramani} and \textit{Y. Zhang} [Math. Proc. Camb. Philos. Soc. 142, No. 1, 111--123 (2007; Zbl 1118.46046)] introduced and studied the notion of pseudo-amenability. In the paper under review, the authors investigate the pseudo-amenability of a semigroup algebra \(\ell^1(S)\) obtaining its equivalence with the amenability of the maximal subgroups of \(S\). As a particular case, they characterize the pseudo-amenability of Brandt semigroup algebras, showing that for a Brandt semigroup \(S={\mathcal{M}}^{0}(G,I)\), the pseudo-amenability of \(\ell ^{1}(S)\) is equivalent to the amenability of \(G\). This characterization of the pseudo-amenability of Brandt semigroup algebras answers a question raised in [\textit{M. M. Sadr}, Commentat. Math. Univ. Carol. 50, No. 3, 413--419 (2009; Zbl 1212.43003)].
reviewed by: Humberto Rafeiro
Mathematics Subject Classification ID: 43A07
Mathematics Subject Classification ID: 20M18
zbMATH DE Number: 5945588
zbMATH Keywords: pseudo-amenability
zbMATH Keywords: \(\ell ^{1}\)-Munn algebra
zbMATH Keywords: Brandt semigroup
author: M. Essmaili
author: Mehdi Rostami
author: Abdolrasoul Pourabbas
MaRDI profile type: Publication
full work available at URL: s00233-010-9278-2
OpenAlex ID: W1976080279
cites work: Biflatness of \(\ell^1\)-semilattice algebras
cites work: Approximate and pseudo-amenability of various classes of Banach algebras
cites work: Banach algebras on semigroups and on their compactifications
cites work: Double centralizer algebras of certain Banach algebras
cites work: Generalized notions of amenability.
cites work: Approximate and pseudo-amenability of the Fourier algebra
cites work: Pseudo-amenable and pseudo-contractible Banach algebras
cites work: Q4846425
cites work: Cohomology in Banach algebras
cites work: Approximate Diagonals and Cohomology of Certain Annihilator Banach Algebras
cites work: Symmetric amenability and the nonexistence of Lie and Jordan derivations
cites work: Biflatness of semigroup algebras
cites work: Pseudo-amenability of Brandt semigroup algebras
cites work: Approximate amenability of Banach category algebras with application to semigroup algebras
DOI: 10.1007/S00233-010-9278-2
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description: scientific article; zbMATH DE number 5945588