Ideals with bounded approximate identities in Fourier algebras.
type: Item
instance of: scholarly article
title: Ideals with bounded approximate identities in Fourier algebras.
zbMATH Open document ID: 1039.46042
DOI: 10.1016/S0022-1236(02)00121-0
published in: Journal of Functional Analysis
publication date: 2003-10-14T00:00:00Z
review text: For a closed subgroup \(H\) of an amenable locally compact group \(G\) the ideal \(I(H)\) in the Fourier algebra \(A(G)\) of \(G\) is shown to have a bounded approximate identity, where for a subset \(E\) of \(G\) the ideal \(I(E)\) is defined by \(\{u\in A(G): u(x)= 0\) for \(x\in E\}\). Moreover, any ideal with a bounded approximate identity is of type \(I(E)\), and all these subsets \(E\) of \(G\) are characterized. Concerning bounds of approximate identities it is shown that for closed subgroups \(H\) in locally nilpotent locally compact groups or in almost connected groups \(G\) with a compact normal subgroup \(K\) such that \(G/K\) is nilpotent the ideal \(I(H)\) has an approximate identity with norm bounded by 2. Generalizations of the above results to the Herz-Figà-Talamanca algebras \(A_p(G)\) are established.
reviewed by: Gerhard Garske
Mathematics Subject Classification ID: 46J20
Mathematics Subject Classification ID: 43A15
Mathematics Subject Classification ID: 46J10
zbMATH DE Number: 1992844
zbMATH Keywords: bounded approximate identity
zbMATH Keywords: Fourier algebra
author: Brian Forrest
author: Eberhard Kaniuth
author: A. T.-M. Lau
author: Nico Spronk
MaRDI profile type: Publication
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full work available at URL: s0022-1236(02)00121-0
OpenAlex ID: W2064017439
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description: scientific article; zbMATH DE number 1992844