Fourier analysis on coset spaces
type: Item
instance of: scholarly article
title: Fourier analysis on coset spaces
zbMATH Open document ID: 0922.43007
published in: Rocky Mountain Journal of Mathematics
publication date: 1999-05-11T00:00:00Z
full work available at URL: CONT281.html
review text: Let \(G\) be a locally compact group with a closed subgroup \(H\). In this paper natural analogs are defined and studied of the Fourier and Fourier-Stieltjes algebras for the homogeneous space \(G/H\) of left cosets of \(H\) in \(G\). In particular, for a compact subgroup \(K\) it is shown that the Fourier algebra \(A(G/K)\) is a regular Banach algebra whose maximal ideal space is \(G/K\), and the amenability of \(G/K\) is characterized in terms of various structural properties of \(A(G/K)\). Moreover, it is proved that \(A(G)\) is weakly amenable for any totally disconnected locally compact group \(G\).
reviewed by: Kokichi Sakai
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 43A07
Mathematics Subject Classification ID: 43A15
zbMATH DE Number: 1286533
zbMATH Keywords: locally compact group
zbMATH Keywords: Fourier-Stieltjes algebras
zbMATH Keywords: homogeneous space
zbMATH Keywords: Fourier algebra
zbMATH Keywords: amenable
author: Brian Forrest
MaRDI profile type: Publication
OpenAlex ID: W2061060390
cites work: Q4141642
cites work: The continuity of derivations of Banach algebras
cites work: On invariant subalgebras of the Fourier-Stieltjes algebra of a locally compact group
cites work: Restrictions of certain function spaces to closed subgroups of locally compact groups
cites work: Q4741034
cites work: L'algèbre de Fourier d'un groupe localement compact
cites work: Moyennes invariantes et représentations unitaires
cites work: Amenability and Derivations of the Fourier Algebra
cites work: Q4022825
cites work: Amenability and bounded approximate identities in ideals of A(G)
cites work: A characterization of weakly amenable Banach algebras
cites work: Harmonic synthesis for subgroups
cites work: Q5723435
cites work: Continuity of module and higher derivations
cites work: Non-Amenability of the Fourier Algebra of a Compact Group
cites work: Remarques sur les ensembles de synthese des algèbres de groupe localement compact
cites work: Properties of the Fourier Algebra That are Equivalent to Amenability
cites work: Impossibilité de la synthèse spectrale sur les groupes abéliens non compacts
cites work: On weak spectral synthesis
cites work: Q3756753
cites work: duality and subgroups
DOI: 10.1216/RMJM/1181071828
description: scientific article; zbMATH DE number 1286533