Multipliers of weighted semigroups and associated Beurling Banach algebras
type: Item
instance of: scholarly article
title: Multipliers of weighted semigroups and associated Beurling Banach algebras
zbMATH Open document ID: 1275.43003
author: S. J. Bhatt
author: H. V. Dedania
author: P. A. Dabhi
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2013-01-10T00:00:00Z
review text: Let \((S,\omega)\) be a weighted discrete abelian semigroup. The \(\omega\)-bounded multipliers on \(S\) form a semigroup \(M_\omega(S)\), on which \(\omega\) induces a natural weight \[ \tilde{\omega}(T):=\sup\left\{\frac{\omega(Ts)}{\omega(s)}:\;s\in S\right\}\quad(T\in M_\omega(S)). \] The authors investigate to what extend various natural (Banach algebraic) properties on \((S,\omega)\) and on its associated Beurling algebra \(\ell^1(S,\omega)\) determine or are determined by the corresponding properties on \((M_\omega(S),\tilde{\omega})\) and on its associated Beurling algebra \(\ell^1(M_\omega(S),\tilde{\omega})\); the case of involutive weighted semigroups with associated \(*\)-Beurling algebras is also considered. To name just a few, the properties studied include semisimplicity, uniqueness of (\(C^*\)-)norm, and (\(*\)-)regularity.
reviewed by: Hung Le Pham
Mathematics Subject Classification ID: 43A20
Mathematics Subject Classification ID: 46J05
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 6124349
zbMATH Keywords: weighted semigroup
zbMATH Keywords: multipliers on a semigroup
zbMATH Keywords: generalized semi-characters
zbMATH Keywords: Beurling algebras
zbMATH Keywords: unique uniform norm property
MaRDI profile type: Publication
full work available at URL: s12044-011-0048-1
OpenAlex ID: W2089177705
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DOI: 10.1007/S12044-011-0048-1
description: scientific article; zbMATH DE number 6124349