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Título:
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The Glicksberg theorem on weakly compact sets for nuclear groups
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Autores:
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Banaszczyk, W ;
Martín Peinador, Elena
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Tipo de documento:
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texto impreso
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Editorial:
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New York Academy of Sciences, 1996
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Topología
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Tipo = Sección de libro
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Resumen:
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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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