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Krein’s Theorem in the Context of Topological Abelian Groups



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Borsich, Tayomara and Domínguez Pérez, Xabier E and Martín Peinador, Elena (2022) Krein’s Theorem in the Context of Topological Abelian Groups. Axioms, 11 (5). p. 224. ISSN 2075-1680

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Official URL: https://doi.org/10.3390/axioms11050224


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.

Item Type:Article
Uncontrolled Keywords:quasi-convex subset; determining subgroup; quasi-convex compactness property; Krein’s Theorem
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:74851
Deposited On:30 Sep 2022 13:45
Last Modified:03 Oct 2022 06:57

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