Extreme non-Arens regularity of the group algebra
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Title
Extreme non-Arens regularity of the group algebraDate
2018-03-01Publisher
De GruyterBibliographic citation
FILALI, M.; GALINDO PASTOR, Jorge (2018). Extreme non-Arens regularity of the group algebra. Forum Mathematicum, v. 30, issue 5, p. 1193–1208Type
info:eu-repo/semantics/articlePublisher version
https://www.degruyter.com/view/j/form.ahead-of-print/forum-2017-0117/forum-2017- ...Version
info:eu-repo/semantics/sumittedVersionSubject
Abstract
The Banach algebras of Harmonic Analysis are usually far from being Arens regular and often turn out to be as irregular as possible. This utmost irregularity has been studied by means of two notions: strong Arens ... [+]
The Banach algebras of Harmonic Analysis are usually far from being Arens regular and often turn out to be as irregular as possible. This utmost irregularity has been studied by means of two notions: strong Arens irregularity, in the sense of Dales and Lau, and extreme non-Arens regularity, in the sense of Granirer. Lau and Losert proved in 1988 that the convolution algebra L1(G) is strongly Arens irregular for any infinite locally compact group. In the present paper, we prove that L1(G) is extremely non-Arens regular for any infinite locally compact group. We actually prove the stronger result that for any non-discrete locally compact group G, there is a linear isometry from L∞(G) into the quotient space L∞(G)/F(G), with F(G) being any closed subspace of L∞(G) made of continuous bounded functions. This, together with the known fact that ℓ∞(G)/WAP(G) always contains a linearly isometric copy of ℓ∞(G), proves that L1(G) is extremely non-Arens regular for every infinite locally compact group [-]
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Forum Mathematicum (2018), v. 30, issue 5Investigation project
Ministerio de Economía y Competitividad (Spain) through project MTM2016-77143-P (AEI/FEDER, UE)Rights
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