Arens regularity of ideals of the group algebra of a compact Abelian group
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Title
Arens regularity of ideals of the group algebra of a compact Abelian groupDate
2023-10-27Publisher
Cambridge University PressISSN
0308-2105; 1473-7124Bibliographic citation
Esmailvandi, R., Filali, M., & Galindo, J. (2023). Arens regularity of ideals of the group algebra of a compact Abelian group. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1–17.Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
Let G be a compact Abelian group and E a subset of the group Gˆ of continuous characters of G . We study Arens regularity-related properties of the ideals L1E(G) of L1(G) that are made of functions ... [+]
Let G be a compact Abelian group and E a subset of the group Gˆ of continuous characters of G . We study Arens regularity-related properties of the ideals L1E(G) of L1(G) that are made of functions whose Fourier transform is supported on E⊆Gˆ . Arens regularity of L1E(G) , the centre of L1E(G)∗∗ and the size of L1E(G)∗/WAP(L1E(G)) are studied. We establish general conditions for the regularity of L1E(G) and deduce from them that L1E(G) is not strongly Arens irregular if E is a small-2 set (i.e. μ∗μ∈L1(G) for every μ∈M1E(G) ), which is not a Λ(1) -set, and it is extremely non-Arens regular if E is not a small-2 set. We deduce also that L1E(G) is not Arens regular when Gˆ∖E is a Lust-Piquard set. [-]
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Proceedings of the Royal Society of Edinburgh Section A: Mathematics (2023)Funder Name
Ministerio de Ciencia e Innovación, Agencia Estatal de Investigación (AEI/10.13039/501100011033) | Universitat Jaume I
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PID2019-106529GB-I00
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