Strongly mixing groups
type: Item
instance of: scholarly article
title: Strongly mixing groups
zbMATH Open document ID: 0873.43006
DOI: 10.1007/BF02676613
author: O. Diekmann
published in: Semigroup Forum
publication date: 1997-06-16T00:00:00Z
full work available at URL: https://eudml.org/doc/135530
review text: Let \(G\) be a totally minimal group, i.e., there does not exist a strictly coarser Hausdorff group topology on \(G\). The author associates to any representation on \(G\) an enveloping semigroup that is weakly almost periodic; hence semigroup theory may be used. If \(G\) is also connected, any unitary representation on \(G\) decomposes into finite-dimensional ones determined by the kernels of the corresponding subrepresentations, with all index coefficients vanishing at infinity. As an application the Fourier-Stieltjes algebra of a totally minimal group is shown to be uniformly dense in the \(C^*\)-algebra formed by all weakly almost periodic functions on the group.
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 43A60
zbMATH DE Number: 1022338
zbMATH Keywords: totally minimal group
zbMATH Keywords: representation
zbMATH Keywords: Fourier-Stieltjes algebra
zbMATH Keywords: almost periodic functions
reviewed by: Jean-Paul Pier
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1022338