Publication: The Glicksberg theorem on weakly compact sets for nuclear groups
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Publication Date
1996
Authors
Banaszczyk, W
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New York Academy of Sciences
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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].
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Proceedings of the 10th Summer Conference held at the Vrije Universiteit, Amsterdam, August 15–18, 1994