Krein’s theorem in the context of topological abelian groups

Borsich, TayomaraDomínguez, XabierMartín Peinador, Elena2022-06-132022-06-132022Borsich, T.; Domínguez, X.; Martín-Peinador, E. Krein’s. Theorem in the Context of Topological Abelian Groups. Axioms 2022, 11, 224. https://doi.org/10.3390/axioms11050224http://hdl.handle.net/2183/30909[Abstract:] 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.engAtribución 3.0 Españahttp://creativecommons.org/licenses/by/3.0/es/Quasi-convex subsetDetermining subgroupQuasi-convex compactness propertyKrein’s TheoremKrein’s theorem in the context of topological abelian groupsjournal articleopen access10.3390/axioms11050224