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 | |