Krein’s Theorem in the Context of Topological Abelian Groups

Borsich, TayomaraDomínguez Pérez, Xabier EMartín Peinador, Elena2023-06-222023-06-222022-05-122075-168010.3390/axioms11050224https://hdl.handle.net/20.500.14352/72089A 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 Españahttps://creativecommons.org/licenses/by/3.0/es/Krein’s Theorem in the Context of Topological Abelian Groupsjournal articlehttps://doi.org/10.3390/axioms11050224https://www.mdpi.com/2075-1680/11/5/224/htmopen accessquasi-convex subsetdetermining subgroupquasi-convex compactness propertyKrein’s TheoremAnálisis funcional y teoría de operadores