Fourier-Stieltjes algebra of a topological group
type: Item
instance of: scholarly article
title: Fourier-Stieltjes algebra of a topological group
zbMATH Open document ID: 1236.22001
author: A. T.-M. Lau
author: Jean Ludwig
published in: Advances in Mathematics
publication date: 2012-03-02T00:00:00Z
review text: Let \(G\) be a topological (not necessarily locally compact) group and let \(B(G)\) denote its Fourier--Stieltjes algebra, i.e. the linear span of the continuous positive definite complex-valued functions on \(G\). The authors describe the basic properties of \(B(G)\) and evaluate its spectrum. In the case, when there is a reasonable notion of the group \(C^*\)-algebra \(A\) for \(G\) (the authors call such \(A\) a host algebra for \(G\); if \(G\) is locally compact then \(A=C^*(G)\)), it is shown that \(B(G)\) is a pre-dual of the universal enveloping von Neumann algebra of \(A\). Finally, \(B(G)\) is calculated when \(G\) is a projective limit of locally compact groups.
Mathematics Subject Classification ID: 22A10
Mathematics Subject Classification ID: 43A30
zbMATH DE Number: 6011380
zbMATH Keywords: topological groups
zbMATH Keywords: unitary representations
zbMATH Keywords: Fourier
zbMATH Keywords: Stieltjes algebra
zbMATH Keywords: Fourier algebra
reviewed by: Vladimir M. Manuilov
MaRDI profile type: Publication
full work available at URL: j.aim.2011.12.022
OpenAlex ID: W2089169620
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DOI: 10.1016/J.AIM.2011.12.022
description: scientific article; zbMATH DE number 6011380