Repositorio de producción científica de la Universidad de Sevilla

Grothendieck locally convex spaces of continuous vector valued functions

Opened Access Grothendieck locally convex spaces of continuous vector valued functions

Citas

buscar en

Estadísticas
Icon
Exportar a
Autor: Freniche Ibáñez, Francisco José
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 1985-12-01
Publicado en: Pacific Journal of Mathematics, 120 (2), 345-355.
Tipo de documento: Artículo
Resumen: 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.
Cita: Freniche Ibáñez, F.J. (1985). Grothendieck locally convex spaces of continuous vector valued functions. Pacific Journal of Mathematics, 120 (2), 345-355.
Tamaño: 1.025Mb
Formato: PDF

URI: http://hdl.handle.net/11441/43496

DOI: 10.2140/pjm.1985.120.345

Mostrar el registro completo del ítem


Esta obra está bajo una Licencia Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 Internacional

Este registro aparece en las siguientes colecciones