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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

## 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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Additional Information: | 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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