Compact right multipliers on a Banach algebra related to locally compact semigroups
type: Item
instance of: scholarly article
title: Compact right multipliers on a Banach algebra related to locally compact semigroups
zbMATH Open document ID: 1246.47010
author: S. Maghsoudi
author: Rasoul Nasr-Isfahani
author: M. J. Mehdipour
published in: Semigroup Forum
publication date: 2012-03-23T00:00:00Z
review text: A locally compact semigroup \(S\) is called compactly cancellative if \(C^{-1}D\) and \(CD^{-1}\) are compact for all compact subsets \(C\) and \(D\) of \(S\). In [Pac. J. Math. 14, 659--664 (1964; Zbl 0135.35803)], \textit{S. Sakai} has proved that, if \(G\) is a locally compact but not compact group, then zero is the only compact right multiplier on the group algebra \(L^{1}(G)\). The main result of this article is a characterization of right compact multipliers on the Banach algebra \(L_{0}^{\infty}(S, M_{a})^{*}\) equipped with an Arens product. This is done by putting together four equivalent definitions of compact right multipliers on \(S\), when \(S\) is a compactly cancellative semigroup with identity. An interesting example is provided at the end to show that there are nontrivial locally compact semigroups for which compact multipliers exist.
reviewed by: Norbert Youmbi
Mathematics Subject Classification ID: 47B48
Mathematics Subject Classification ID: 43A22
zbMATH DE Number: 6018263
zbMATH Keywords: Arens product
zbMATH Keywords: compact operator
zbMATH Keywords: right multiplier
zbMATH Keywords: locally compact semigroups
MaRDI profile type: Publication
full work available at URL: s00233-011-9312-z
OpenAlex ID: W2083334589
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DOI: 10.1007/S00233-011-9312-Z
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description: scientific article; zbMATH DE number 6018263