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Grothendieck locally convex spaces of continuous vector valued functions

 

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dc.creator Freniche Ibáñez, Francisco José es
dc.date.accessioned 2016-07-12T07:52:17Z
dc.date.available 2016-07-12T07:52:17Z
dc.date.issued 1985-12-01
dc.identifier.citation Freniche Ibáñez, F.J. (1985). Grothendieck locally convex spaces of continuous vector valued functions. Pacific Journal of Mathematics, 120 (2), 345-355.
dc.identifier.issn 0030-8730 es
dc.identifier.issn 1945-5844 es
dc.identifier.uri http://hdl.handle.net/11441/43496
dc.description.abstract Let ^{X, E) be the space of continuous functions from the completely regular Hausdorff space X into the Hausdorff locally convex space E, endowed with the compact-open topology. Our aim is to characterize the ^(X, E) spaces which have the following property: weak-star and weak sequential convergences coincide in the equicontinuous subsets of ^(X, E)'. These spaces are here called Grothendieck spaces. It is shown that in the equicontinuous subsets of E' the σ(E', E)- and β(E', ^-sequential convergences coincide, if ^(X, E) is a Grothendieck space and X contains an infinite compact subset. Conversely, if X is a G-space and E is a strict inductive limit of Frechet-Montel spaces ^(X, E) is a Grothendieck space. Therefore, it is proved that if £ is a separable Frechet space, then E is a Montel space if and only if there is an infinite compact Hausdorff X such that , E) is a Grothendieck space. es
dc.format application/pdf es
dc.language.iso eng es
dc.publisher Mathematical Sciences Publishers es
dc.relation.ispartof Pacific Journal of Mathematics, 120 (2), 345-355.
dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional *
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ *
dc.title Grothendieck locally convex spaces of continuous vector valued functions es
dc.type info:eu-repo/semantics/article es
dc.type.version info:eu-repo/semantics/publishedVersion es
dc.rights.accessrights info:eu-repo/semantics/openAccess es
dc.contributor.affiliation Universidad de Sevilla. Departamento de Análisis Matemático es
dc.relation.publisherversion http://dx.doi.org/10.2140/pjm.1985.120.345 es
dc.identifier.doi 10.2140/pjm.1985.120.345 es
dc.contributor.group Universidad de Sevilla. FQM104: Analisis Matematico es
idus.format.extent 11 p. es
dc.journaltitle Pacific Journal of Mathematics es
dc.publication.volumen 120 es
dc.publication.issue 2 es
dc.publication.initialPage 345 es
dc.publication.endPage 355 es
dc.identifier.idus https://idus.us.es/xmlui/handle/11441/43496
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