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Krein’s theorem in the context of topological abelian groups
dc.contributor.author | Borsich, Tayomara | |
dc.contributor.author | Domínguez, Xabier | |
dc.contributor.author | Martín Peinador, Elena | |
dc.date.accessioned | 2022-06-13T18:08:20Z | |
dc.date.available | 2022-06-13T18:08:20Z | |
dc.date.issued | 2022 | |
dc.identifier.citation | Borsich, 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/axioms11050224 | es_ES |
dc.identifier.uri | http://hdl.handle.net/2183/30909 | |
dc.description.abstract | [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. | es_ES |
dc.description.sponsorship | Agencia Estatal de Investigación (AEI); MTM2016-79422-P | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | MDPI | es_ES |
dc.relation.uri | https://doi.org/10.3390/axioms11050224 | es_ES |
dc.rights | Atribución 3.0 España | es_ES |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/es/ | * |
dc.subject | Quasi-convex subset | es_ES |
dc.subject | Determining subgroup | es_ES |
dc.subject | Quasi-convex compactness property | es_ES |
dc.subject | Krein’s Theorem | es_ES |
dc.title | Krein’s theorem in the context of topological abelian groups | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.rights.access | info:eu-repo/semantics/openAccess | es_ES |
UDC.journalTitle | Axioms | es_ES |
UDC.volume | 11 | es_ES |
UDC.issue | 5 | es_ES |
UDC.startPage | 224 | es_ES |
dc.identifier.doi | 10.3390/axioms11050224 |
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