The dual space of precompact groups

M. Ferrer; S. Hernández; V. Uspenskij

Commentationes Mathematicae Universitatis Carolinae (2013)

  • Volume: 54, Issue: 2, page 239-244
  • ISSN: 0010-2628

Abstract

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For any topological group G the dual object G ^ is defined as the set of equivalence classes of irreducible unitary representations of G equipped with the Fell topology. If G is compact, G ^ is discrete. In an earlier paper we proved that G ^ is discrete for every metrizable precompact group, i.e. a dense subgroup of a compact metrizable group. We generalize this result to the case when G is an almost metrizable precompact group.

How to cite

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Ferrer, M., Hernández, S., and Uspenskij, V.. "The dual space of precompact groups." Commentationes Mathematicae Universitatis Carolinae 54.2 (2013): 239-244. <http://eudml.org/doc/252527>.

@article{Ferrer2013,
abstract = {For any topological group $G$ the dual object $\widehat\{G\}$ is defined as the set of equivalence classes of irreducible unitary representations of $G$ equipped with the Fell topology. If $G$ is compact, $\widehat\{G\}$ is discrete. In an earlier paper we proved that $\widehat\{G\}$ is discrete for every metrizable precompact group, i.e. a dense subgroup of a compact metrizable group. We generalize this result to the case when $G$ is an almost metrizable precompact group.},
author = {Ferrer, M., Hernández, S., Uspenskij, V.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {compact group; precompact group; representation; Pontryagin--van Kampen duality; compact-open topology; Fell dual space; Fell topology; Kazhdan property (T); precompact group; Fell dual space},
language = {eng},
number = {2},
pages = {239-244},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The dual space of precompact groups},
url = {http://eudml.org/doc/252527},
volume = {54},
year = {2013},
}

TY - JOUR
AU - Ferrer, M.
AU - Hernández, S.
AU - Uspenskij, V.
TI - The dual space of precompact groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2013
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 2
SP - 239
EP - 244
AB - For any topological group $G$ the dual object $\widehat{G}$ is defined as the set of equivalence classes of irreducible unitary representations of $G$ equipped with the Fell topology. If $G$ is compact, $\widehat{G}$ is discrete. In an earlier paper we proved that $\widehat{G}$ is discrete for every metrizable precompact group, i.e. a dense subgroup of a compact metrizable group. We generalize this result to the case when $G$ is an almost metrizable precompact group.
LA - eng
KW - compact group; precompact group; representation; Pontryagin--van Kampen duality; compact-open topology; Fell dual space; Fell topology; Kazhdan property (T); precompact group; Fell dual space
UR - http://eudml.org/doc/252527
ER -

References

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  11. Ferrer M.V., Hernández S., Dual topologies on groups, Topology Appl.(to appear). MR2921826
  12. Ferrer M.V., Hernández S., Uspenskij V., Precompact groups and property ( T ) , arXiv:1112.1350. MR3045168
  13. de la Harpe P., Valette A., La propriété ( T ) de Kazhdan pour les groupes localement compacts, Astérisque 175, Soc. Math. France, 1989. Zbl0759.22001
  14. Hernández S., Macario S., Trigos-Arrieta F.J., 10.1016/j.jmaa.2008.07.065, J. Math. Anal. Appl. 348 (2008), no. 2, 834–842. Zbl1156.22002MR2446038DOI10.1016/j.jmaa.2008.07.065
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