Compacidad débil en espacios de funciones integrables-Bochner, y la propiedad de Radon-Nikodym.
Compacité par compensation
Compact sets in
Compactness and countable compactness in weak topologies
A bounded closed convex set K in a Banach space X is said to have quasi-normal structure if each bounded closed convex subset H of K for which diam(H) > 0 contains a point u for which ∥u-x∥ < diam(H) for each x ∈ H. It is shown that if the convex sets on the unit sphere in X satisfy this condition (which is much weaker than the assumption that convex sets on the unit sphere are separable), then relative to various weak topologies, the unit ball in X is compact whenever it is countably compact....
Compactness in certain abstract function spaces with application to differential inclusions
In this note we present a result on compactness in certain Banach spaces of vector valued functions. We demonstrate an application of this result to the questions of existence of solutions of nonlinear differential inclusions on a Banach space.
Compactness in the First Baire Class and Baire-1 Operators
For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1 (M, E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in case E = R, also hold true in the general case. For instance: a subset of B1 (M, E) is compact iff it is sequentially (resp. countably) compact, the convex hull of a compact bounded subset of B1 (M,...
Compactoid sets in p-adic locally convex spaces
Contribuciones al análisis funcional no-standard.
En este trabajo presentamos aportaciones al tratamiento no-standard del Análisis Funcional en dos direcciones. En la sección 2 la envoltura no-standard de un espacio vectorial topológico, introducida por Luxemburg [7] y por Henson y Moore [2] se aplica al caso de un álgebra topológica. En las secciones 3 y 4 se dan caracterizaciones de elementos accesibles (pre-near-standard) y casi-standard (near-standard) en espacios vectoriales topológicos en términos de una familia filtrante densa de subespacios...
Convex-compact sets and Banach discs
Every relatively convex-compact convex subset of a locally convex space is contained in a Banach disc. Moreover, an upper bound for the class of sets which are contained in a Banach disc is presented. If the topological dual of a locally convex space is the -closure of the union of countably many -relatively countably compacts sets, then every weakly (relatively) convex-compact set is weakly (relatively) compact.
Countably determined locally convex spaces
Criteria for Eberlein Compactness in Spaces of Continuous Functions.