%0 Journal Article
%A Borsich, Tayomara
%A Domínguez Pérez, Xabier E
%A Martín Peinador, Elena
%T Krein’s Theorem in the Context of Topological Abelian Groups
%D 2022
%@ 2075-1680
%U https://hdl.handle.net/20.500.14352/72089
%X A topological abelian group G is said to have the quasi-convex compactness property (briefly, qcp) if the quasi-convex hull of every compact subset of G is again compact. In this paper we prove that there exist locally quasi-convex metrizable complete groups G which endowed with the weak topology associated to their character groups G∧, do not have the qcp. Thus, Krein’s Theorem, a well known result in the framework of locally convex spaces, cannot be fully extended to locally quasi-convex groups. Some features of the qcp are also studied.
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