The dual of semigroup algebras with certain locally convex topologies
type: Item
instance of: scholarly article
title: The dual of semigroup algebras with certain locally convex topologies
zbMATH Open document ID: 1112.43001
published in: Semigroup Forum
publication date: 2007-03-20T00:00:00Z
review text: Let \(S\) be a locally compact semigroup, \(M(S)\) the Banach space of all bounded complex regular Borel measures on \(S\), \(M_a(S)\) the space of all \(\mu \in M(S)\) for which the maps \(x \to \delta_x * | \mu| \) and \(x \to | \mu| *\delta_x\) from \(S\) into \(M(S)\) are weakly continuous, \(\delta_x\) denotes the Dirac measure at \(x\). For an extensive class of locally compact semigroups \(S\), a locally convex topology on \(M_a(S)\) is introduced so that the Banach space \(L^\infty_0 (S,M_a(S))\) can be identified with its strong dual. It is shown that, except for the case when \(S\) is finite, there are infinitely many such locally convex topologies \(\tau\) on \(M_a(S)\). The spectrum of \((M_a(S), \tau )\) is characterized in terms of semicharacters on \(S\).
Mathematics Subject Classification ID: 43A10
Mathematics Subject Classification ID: 43A15
Mathematics Subject Classification ID: 46A03
zbMATH DE Number: 5134745
zbMATH Keywords: locally compact semigroups
zbMATH Keywords: locally convex topology
zbMATH Keywords: semigroup algebra
author: S. Maghsoudi
author: Rasoul Nasr-Isfahani
author: A. Rejali
reviewed by: Boris Rubin
MaRDI profile type: Publication
full work available at URL: s00233-006-0660-z
OpenAlex ID: W2139595519
DOI: 10.1007/S00233-006-0660-Z
description: scientific article; zbMATH DE number 5134745