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dc.contributor.authorFilali, M.
dc.contributor.authorGalindo, Jorge
dc.date.accessioned2018-11-28T07:54:14Z
dc.date.available2018-11-28T07:54:14Z
dc.date.issued2018-03-01
dc.identifier.citationFILALI, M.; GALINDO PASTOR, Jorge (2018). Extreme non-Arens regularity of the group algebra. Forum Mathematicum, v. 30, issue 5, p. 1193–1208ca_CA
dc.identifier.urihttp://hdl.handle.net/10234/177714
dc.description.abstractThe 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 groupca_CA
dc.format.extent20 p.ca_CA
dc.format.mimetypeapplication/pdfca_CA
dc.language.isoengca_CA
dc.publisherDe Gruyterca_CA
dc.relation.isPartOfForum Mathematicum (2018), v. 30, issue 5ca_CA
dc.rights.urihttp://rightsstatements.org/vocab/CNE/1.0/*
dc.subjectGroup algebraca_CA
dc.subjectExtremely non-Arens regularca_CA
dc.subjectWeakly almost periodicca_CA
dc.subjectIsometryca_CA
dc.subjectHaar homeomorphismca_CA
dc.subjectMetrizable groupsca_CA
dc.titleExtreme non-Arens regularity of the group algebraca_CA
dc.typeinfo:eu-repo/semantics/articleca_CA
dc.identifier.doihttps://doi.org/10.1515/forum-2017-0117
dc.relation.projectIDMinisterio de Economía y Competitividad (Spain) through project MTM2016-77143-P (AEI/FEDER, UE)ca_CA
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessca_CA
dc.relation.publisherVersionhttps://www.degruyter.com/view/j/form.ahead-of-print/forum-2017-0117/forum-2017-0117.xmlca_CA
dc.contributor.funderPartially supported by Väisälä Foundation in 2012–2014ca_CA
dc.type.versioninfo:eu-repo/semantics/sumittedVersionca_CA


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