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The Glicksberg theorem on weakly compact sets for nuclear groups

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Banaszczyk, W and Martín Peinador, Elena (1996) The Glicksberg theorem on weakly compact sets for nuclear groups. In Papers on general topology and applications. Annals of the New York Academy of Sciences (788). New York Academy of Sciences, New York, pp. 34-39. ISBN 0-89766-964-9

Official URL: http://onlinelibrary.wiley.com/doi/10.1111/j.1749-6632.1996.tb36794.x/abstract


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Abstract

By the weak topology on an Abelian topological group we mean the topology induced by the family of all continuous characters. A well-known theorem of I. Glicksberg says that weakly compact subsets of locally compact Abelian (LCA) groups are compact. D. Remus and F.J. Trigos-Arrieta [1993. Proceedings Amer. Math. Soc. 117] observed that Glicksberg's theorem remains valid for closed subgroups of any product of LCA groups. Here we show that, in fact, it remains valid for all nuclear groups, a class of Abelian topological groups introduced by the first author in the monograph, “Additive subgroups of topological vector spaces” [1991. Lecture Notes in Math. 1466].


Item Type:Book Section
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Proceedings of the 10th Summer Conference held at the Vrije Universiteit, Amsterdam, August 15–18, 1994

Uncontrolled Keywords:Glicksberg's theorem; nuclear groups; LCA groups
Subjects:Sciences > Mathematics > Topology
ID Code:21720
Deposited On:06 Jun 2013 16:39
Last Modified:12 Dec 2018 15:13

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