Weakly pseudocompact subsets of nuclear groups

Let G be an Abelian topological group and G(+) the group G endowed with the weak topology induced by continuous characters. We say that G respects com pactness (pseudocompactness, countable compactness, functional boundedness) if G and G+ have the same compact (pseudocompact, countably compact, funct ionally bounded) sets. The well-known theorem of Glicksberg that LCA groups respect compactness was extended by Trigos-Arrieta to pseudocompactness an d functional boundedness. In this paper we generalize these results to arbi trary nuclear groups, a class of Abelian topological groups which contains LCA groups and nuclear locally convex spaces and is closed with respect to subgroups, separated quotients and arbitrary products. (C) 1999 Elsevier Sc ience B.V. All rights reserved.