Figa-Talamanca-Herz algebras for restricted inverse semigroups and Clifford semigroups
type: Item
instance of: scholarly article
title: Figa-Talamanca-Herz algebras for restricted inverse semigroups and Clifford semigroups
zbMATH Open document ID: 1257.43004
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-08-30T00:00:00Z
review text: The authors develop the Figa-Talamanca-Herz algebras and the space of \(p\)-pseudomeasures to inverse semigroups with restricted semigroup algebras. Let \(1 < p, q < \infty\) be such that \(\frac{1}{p}+\frac{1}{q}=1\). The Banach algebra of \(p\)-pseudomeasures \(PM_{p} (S)\) and the Figa-Talamanca-Herz algebras \(A_{q} (S)\) are defined and it is shown that \(A_{q} (S)^*= PM_{p} (S)\). Moreover, \(PM_{p} (S)\), \(A_{q} (S)\) are characterized for the Clifford semigroup in the sense of \(p\)-pseudomeasures and Figa-Talamanca-Herz algebras of maximal subgroups of \(S\), respectively. Also, it is shown that the character space of \(A_{q} (S)\) is equal to \(S\) for a Clifford semigroup \(S\). As an example of these Banach algebras and restricted semigroup algebras, the authors discuss locally finite inverse semigroups.
reviewed by: Bolis Basit
Mathematics Subject Classification ID: 43A10
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 47L30
zbMATH DE Number: 6074397
zbMATH Keywords: Figa-Talamanca-Herz algebras
zbMATH Keywords: semigroup algebras
zbMATH Keywords: Clifford semigroups
zbMATH Keywords: representations
zbMATH Keywords: pseudomeasures
author: Ali Reza Medghalchi
author: Hasan Pourmahmood Aghababa
MaRDI profile type: Publication
full work available at URL: j.jmaa.2012.05.043
OpenAlex ID: W1993143109
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DOI: 10.1016/J.JMAA.2012.05.043
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description: scientific article; zbMATH DE number 6074397