Please use this identifier to cite or link to this item: https://hdl.handle.net/11000/30586
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dc.contributor.authorFerrando, Juan Carlos-
dc.contributor.authorGabriyelyan, Saak-
dc.contributor.authorKa̧kol, Jerzy-
dc.contributor.otherDepartamentos de la UMH::Estadística, Matemáticas e Informáticaes_ES
dc.date.accessioned2024-01-23T15:29:36Z-
dc.date.available2024-01-23T15:29:36Z-
dc.date.created2019-12-
dc.identifier.citationMathematische Nachrichten Volume 292, Issue12, (2019), p.2602-2618es_ES
dc.identifier.issn1522-2616-
dc.identifier.issn0025-584X-
dc.identifier.urihttps://hdl.handle.net/11000/30586-
dc.description.abstractFor wide classes of locally convex spaces, in particular, for the space 𝐶𝑝(𝑋) of continuous real-valued functions on a Tychonoff space 𝑋 equipped with the pointwise topology, we characterize the existence of a fundamental bounded resolution (i.e., an increasing family of bounded sets indexed by the irrationals which swallows the bounded sets). These facts together with some results from Grothendieck’s theory of (𝐷𝐹)-spaces have led us to introduce quasi-(𝐷𝐹)-spaces, a class of locally convex spaces containing (𝐷𝐹)-spaces that preserves subspaces, countable direct sums and countable products. Regular (𝐿𝑀)-spaces as well as their strong duals are quasi- (𝐷𝐹)-spaces. Hence the space of distributions 𝐷′(Ω) provides a concrete example of a quasi-(𝐷𝐹)-space not being a (𝐷𝐹)-space. We show that 𝐶𝑝(𝑋) has a fundamental bounded resolution if and only if 𝐶𝑝(𝑋) is a quasi-(𝐷𝐹)-space if and only if the strong dual of 𝐶𝑝(𝑋) is a quasi-(𝐷𝐹)-space if and only if 𝑋 is countable. If 𝑋 is metrizable, then 𝐶𝑘(𝑋) is a quasi-(𝐷𝐹)-space if and only if 𝑋 is a 𝜎-compact Polish space.es_ES
dc.formatapplication/pdfes_ES
dc.format.extent17es_ES
dc.language.isoenges_ES
dc.publisherWileyes_ES
dc.rightsinfo:eu-repo/semantics/openAccesses_ES
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectbounded resolutiones_ES
dc.subjectclass 𝔊es_ES
dc.subject(𝐷𝐹)-spacees_ES
dc.subjectfree locally convex spacees_ES
dc.subjectpointwise topologyes_ES
dc.subjectquasi-(𝐷𝐹)- spacees_ES
dc.subject.otherCDU::5 - Ciencias puras y naturales::51 - Matemáticases_ES
dc.titleBounded sets structure of 𝑪𝒑 (𝑿) and quasi-(𝑫𝑭)-spaceses_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.contributor.instituteInstitutos de la UMH::Instituto Centro de Investigación Operativaes_ES
dc.relation.publisherversionhttps://doi.org/10.1002/mana.201800085es_ES
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