Amenability and bounded approximate identities in ideals of A(G)
type: Item
instance of: scholarly article
title: Amenability and bounded approximate identities in ideals of A(G)
zbMATH Open document ID: 0712.43002
published in: Illinois Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: Let G be a locally compact group and A(G) the Fourier algebra. The author investigates under which condition a closed ideal J of A(G) possesses a bounded approximate identity (b.a.i.). This is related to amenability. E.g. G is amenable iff \(J_ e=\{f\in A(G):\) \(f(e)=0\}\) has a b.a.i. The same question is treated for \(W^*\)-closed and cofinal ideals. It is shown that G is amenable iff each homomorphism from A(G) with finite dimensional range is continuous. Finally, Banach modules, and, in particular, VN(G) as A(G)-module, are studied.
reviewed by: Wolfgang Arendt
Mathematics Subject Classification ID: 43A07
Mathematics Subject Classification ID: 43A22
zbMATH DE Number: 4171654
zbMATH Keywords: locally compact group
zbMATH Keywords: Fourier algebra
zbMATH Keywords: closed ideal
zbMATH Keywords: bounded approximate identity
zbMATH Keywords: amenability
zbMATH Keywords: homomorphism
author: Brian Forrest
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4171654