A characterization of the closed unital ideals of the Fourier-Stieltjes algebra \(B\)(\(G\)) of a locally compact amenable group \(G\).
type: Item
instance of: scholarly article
title: A characterization of the closed unital ideals of the Fourier-Stieltjes algebra \(B\)(\(G\)) of a locally compact amenable group \(G\).
zbMATH Open document ID: 1047.43009
DOI: 10.1016/S0022-1236(03)00143-5
published in: Journal of Functional Analysis
publication date: 2004-02-03T00:00:00Z
review text: Let \(G\) be a locally compact abelian group, \(L^1(G)\) be its group algebra and \(M(G)\) be its measure algebra. Let \(\mu\in M(G)\) be a given measure. The Glicksberg-Host-Parreau theorem [cf. \textit{B. Host} and \textit{F. Parreau}, Ann. Inst. Fourier 28, 143--164 (1978; Zbl 0368.43001)] states that the ideal \(\mu\ast L^1(G)\) is closed in \(L^1(G)\) iff \(\mu\) is the product of an invertible measure and an idempotent measure. This theorem is equivalent to the statement: A closed ideal \(I\) of \(M(G)\) is unital iff it is of the form \(I=\mu\ast M(G)\) for some measure \(\mu\in M(G)\). The aim of this paper is to establish a similar theorem for the Fourier-Stieltjes algebra \(B(G)\) of a locally compact amenable group \(G\). The author presents the following result: A closed ideal \(I\) of \(M(G)\) is unital iff \(I\) is a principal ideal. -- The paper also contains an abstract version of this result.
Mathematics Subject Classification ID: 43A22
Mathematics Subject Classification ID: 46J10
Mathematics Subject Classification ID: 47B48
zbMATH DE Number: 2037124
zbMATH Keywords: multiplier
zbMATH Keywords: Fourier algebra
zbMATH Keywords: Fourier-Stieltjes algebra
author: A. Ülger
reviewed by: Saulius Norvidas
MaRDI profile type: Publication
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full work available at URL: s0022-1236(03)00143-5
OpenAlex ID: W1987282124
description: scientific article; zbMATH DE number 2037124