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dc.contributor.authorFerrer González, María Vicenta
dc.contributor.authorHernández Muñoz, Salvador
dc.contributor.authorTárrega Ruiz, Luis
dc.date.accessioned2018-09-24T09:09:19Z
dc.date.available2018-09-24T09:09:19Z
dc.date.issued2018-08
dc.identifier.citationFERRER, María V.; HERNÁNDEZ, Salvador; TÁRREGA, Luis. A dichotomy property for locally compact groups. Journal of Functional Analysis, 2018, 275.4: 869-891.ca_CA
dc.identifier.urihttp://hdl.handle.net/10234/176206
dc.description.abstractWe extend to metrizable locally compact groups Rosenthal's theorem describing those Banach spaces containing no copy of l1. For that purpose, we transfer to general locally compact groups the notion of interpolation (Io) set, which was defined by Hartman and Ryll-Nardzewsky for locally compact abelian groups. Thus we prove that for every sequence [gn]n<w in a locally compact group G, then either [gn]n<w has a weak Cauchy subsequence or contains a subsequence that is an Io set. This result is subsequently applied to obtain sufficient conditions for the existence of Sidon sets in a locally compact group G, an old question that remains open since 1974. Finally, we show that every locally compact group strongly respects compactness extending thereby a result by Comfort, Trigos-Arrieta, and Wu [13], who established this property for abelian locally compact groups.ca_CA
dc.format.extent22 p.ca_CA
dc.format.mimetypeapplication/pdfca_CA
dc.language.isoengca_CA
dc.publisherElsevierca_CA
dc.rights© 2018 Elsevier Inc. All rights reserved.ca_CA
dc.subjectlocally compact groupca_CA
dc.subject(Io) setca_CA
dc.subjectSidon setca_CA
dc.subjectWeak topologyca_CA
dc.titleA dichotomy property for locally compact groupsca_CA
dc.typeinfo:eu-repo/semantics/articleca_CA
dc.identifier.doihttps://doi.org/10.1016/j.jfa.2018.03.013
dc.relation.projectIDSpanish Ministerio de Economía y Competitividad, grant MTM2016-77143-P (AEI/FEDER, EU) ; Universitat Jaume I (grant P1171B2015-77) ; Generalitat Valenciana (PROMETEO/2014/062)ca_CA
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessca_CA
dc.relation.publisherVersionhttps://www.sciencedirect.com/science/article/pii/S0022123618301228ca_CA
dc.type.versioninfo:eu-repo/semantics/draftca_CA


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