On ideals in the bidual of the Fourier algebra and related algebras
type: Item
instance of: scholarly article
title: On ideals in the bidual of the Fourier algebra and related algebras
zbMATH Open document ID: 1201.43001
author: Matthias Neufang
author: M. Filali
author: M. Sangani Monfared
published in: Journal of Functional Analysis
publication date: 2010-05-17T00:00:00Z
review text: For a nonmetrizable compact group \(G\) whose local weight \(b(G)\) has uncountable cofinality and an amenable locally compact group \(H\), let \(A(G\times H)\) be the Fourier algebra of \(G\times H\) and \(UC_2(G\times H)\) be the space of uniformly continuous functionals in the group von Neumann algebra \(VN(G\times H)\) of \(G\times H\). In this paper, the authors show that there exist at least \(2^{2^{b(G)}}\) left ideals of dimensions at least \(2^{2^{b(G)}}\) in \(A(G\times H)^{**}\) and in \(UC_2(G\times H)^*\). It is also proved that every nontrivial right ideal in \(A(G\times H)^{**}\) and in \(UC_2(G\times H)^*\) has dimension at least \(2^{2^{b(G)}}\).
reviewed by: Tianxuan Miao
Mathematics Subject Classification ID: 43A10
zbMATH DE Number: 5708600
zbMATH Keywords: amenable groups
zbMATH Keywords: compact nonmetrizable groups
zbMATH Keywords: group von Neumann algebra
zbMATH Keywords: factorization
zbMATH Keywords: double dual of Fourier algebra
zbMATH Keywords: dual of uniformly continuous functionals
zbMATH Keywords: unitary representations
zbMATH Keywords: one-sided ideals
zbMATH Keywords: cancellable sets
MaRDI profile type: Publication
full work available at URL: j.jfa.2009.12.011
OpenAlex ID: W2044597278
cites work: Some Results on the Center of an Algebra of Operators on VN(G) for the Heisenberg group
cites work: Topological Invariant Means on the Von Neumann Algebra VN(G)
cites work: The second conjugate space of a Banach algebra as an algebra
cites work: On the ideal structure of some Banach algebras related to convolution operators on \(L^{p}(G)\)
cites work: L'algèbre de Fourier d'un groupe localement compact
cites work: Weak factorizations of operators in the group von Neumann algebras of certain amenable groups and applications
cites work: RIGHT CANCELLATION IN THE ${\cal L}{\cal U}{\cal C}$ -COMPACTIFICATION OF A LOCALLY COMPACT GROUP
cites work: One-sided ideals and right cancellation in the second dual of the group algebra and similar algebras
cites work: Isometric Isomorphisms Between Banach Algebras Related to Locally Compact Groups
cites work: Q5615626
cites work: Algebra in the Stone-Čech compactification: theory and applications
cites work: On the set of topologically invariant means on the von Neumann algebra \(VN(G)\)
cites work: Continuity of Arens multiplication on the dual space of bounded uniformly continuous functions on locally compact groups and topological semigroups
cites work: Uniformly continuous functionals on Banach algebras
cites work: The \(C^ \ast\)-algebra generated by operators with compact support on a locally compact group
cites work: A unified approach to the topological centre problem for certain Banach algebras arising in abstract harmonic analysis
cites work: Invariant Means on a Class of Von Neumann Algebras
cites work: The number of cofinal ultrafilters
DOI: 10.1016/J.JFA.2009.12.011
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description: scientific article; zbMATH DE number 5708600