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dc.contributor.authorFerrer González, María Vicenta
dc.contributor.authorHernández Muñoz, Salvador
dc.contributor.authorUspenskij, Vladimir
dc.identifier.citationFERRER, M.; HERNÁNDEZ, S.; USPENSKIJ, V. Precompact groups and property (T). Journal of Mathematical Analysis and Applications, 2013, 404.2: 221-230.ca_CA
dc.description.abstractFor a topological group GG, the dual object View the MathML sourceĜ is defined as the set of equivalence classes of irreducible unitary representations of GG equipped with the Fell topology. It is well known that, if GG is compact, View the MathML sourceĜ is discrete. In this paper, we investigate to what extent this remains true for precompact groups, that is, dense subgroups of compact groups. We show that: (a) if GG is a metrizable precompact group, then View the MathML sourceĜ is discrete; (b) if GG is a countable non-metrizable precompact group, then View the MathML sourceĜ is not discrete; (c) every non-metrizable compact group contains a dense subgroup GG for which View the MathML sourceĜ is not discrete. This extends to the non-Abelian case what was known for Abelian groups. We also prove that, if GG is a countable Abelian precompact group, then GG does not have Kazhdan’s property (T), although View the MathML sourceĜ is discrete if GG is metrizable.ca_CA
dc.format.extent9 p.ca_CA
dc.relation.isPartOfJournal of Mathematical Analysis and Applications Volume 404, Issue 2, 15 August 2013ca_CA
dc.rights(c) Elsevierca_CA
dc.subjectCompact groupca_CA
dc.subjectPrecompact groupca_CA
dc.subjectPontryagin–van Kampen dualityca_CA
dc.subjectCompact-open topologyca_CA
dc.subjectFell dual spaceca_CA
dc.subjectFell topologyca_CA
dc.subjectBohr compactificationca_CA
dc.subjectKazhdan property (T)ca_CA
dc.subjectDetermined groupca_CA
dc.titlePrecompact groups and property (T)ca_CA

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