RT Book, Section
T1 The Glicksberg theorem on weakly compact sets for nuclear groups
A1 Banaszczyk, W
A1 Martín Peinador, Elena
A2 Coplakova, Eva
A2 Hart, Klaas Pieter
AB 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].
PB New York Academy of Sciences
SN 0-89766-964-9
YR 1996
FD 1996
LK https://hdl.handle.net/20.500.14352/60702
UL https://hdl.handle.net/20.500.14352/60702
NO Proceedings of the 10th Summer Conference held at the Vrije Universiteit, Amsterdam, August 15–18, 1994
NO KBN
NO D.G.I.C.Y.T.
DS Docta Complutense
RD 9 abr 2025