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On spaces C^{b}(X) weakly K-analytic

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On spaces C^{b}(X) weakly K-analytic

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dc.contributor.author Carlos Ferrando, Juan es_ES
dc.contributor.author Kakol, Jerzy es_ES
dc.contributor.author López Pellicer, Manuel es_ES
dc.date.accessioned 2018-06-01T04:20:51Z
dc.date.available 2018-06-01T04:20:51Z
dc.date.issued 2017 es_ES
dc.identifier.issn 0025-584X es_ES
dc.identifier.uri http://hdl.handle.net/10251/103128
dc.description.abstract [EN] A subset Y of the dual closed unit ball B_{E*} of a Banach space E is called a Rainwater set for E if every bounded sequence of E that converges pointwise on Y converges weakly in E. In this paper, topological properties of Rainwater sets for the Banach space C^{b}(X) of the real-valued continuous and bounded functions defined on a completely regular space X equipped with the supremum-norm are studied. This applies to characterize the weak K-analyticity of C^{b}(X) in terms of certain Rainwater sets for C^{b}(X). Particularly, we show that C^{b}(X) is weakly K-analytic if and only if there exists a Rainwater set Y for C^{b}(X) such that (C^{b}(X),sigma_{Y}) is both K-analytic and angelic, where sigma_{Y} denotes the topology on C^{b}(X) of the pointwise convergence on Y. For the case when X is compact, one gets classic Talagrand¿s theorem. As an application we show that if X is a compact space and Y is a G_{delta}-dense subspace, then X is Talagrand compact, i.e., C^{p}(X)) is K-analytic, if and only if the space (C(X),sigma_{Y}) is K-analytic. es_ES
dc.description.sponsorship Conselleria d'Educacio, Investigacio, Cultura i Esports of Generalitat Valenciana, Grant, PROMETEO/2013/058; Prague, Institute of Mathematics, Academy of Sciences of the Czech Republic, Grant, GACR project 16-34860L, RVO: 67985840 en_EN
dc.language Inglés es_ES
dc.publisher John Wiley & Sons es_ES
dc.relation.ispartof Mathematische Nachrichten es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Pseudocompact space es_ES
dc.subject K-analytic space es_ES
dc.subject Rainwater set es_ES
dc.subject Talagrand compact set es_ES
dc.subject Lindelof sigma-space es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title On spaces C^{b}(X) weakly K-analytic es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1002/mana.201600396 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2013%2F058/ es_ES
dc.rights.accessRights Cerrado es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Carlos Ferrando, J.; Kakol, J.; López Pellicer, M. (2017). On spaces C^{b}(X) weakly K-analytic. Mathematische Nachrichten. 290(16):2612-2618. https://doi.org/10.1002/mana.201600396 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1002/mana.201600396 es_ES
dc.description.upvformatpinicio 2612 es_ES
dc.description.upvformatpfin 2618 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 290 es_ES
dc.description.issue 16 es_ES
dc.relation.pasarela S\348433 es_ES
dc.contributor.funder Generalitat Valenciana es_ES


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