Article
Dieudonné-Köthe duality for vector-valued function spaces: localization of bounded sets and barrelledness
Author/s | Florencio Lora, Miguel
Mayoral Masa, Fernando Paúl Escolano, Pedro José |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Publication Date | 2010 |
Deposit Date | 2021-09-13 |
Published in |
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Abstract | We study Dieudonné-Köthe spaces of Lusin-measurable functions with values in a locally convex space. Let Λ be a solid locally convex lattice of scalar-valued measurable functions defined on a measure space Ω. If E is a ... We study Dieudonné-Köthe spaces of Lusin-measurable functions with values in a locally convex space. Let Λ be a solid locally convex lattice of scalar-valued measurable functions defined on a measure space Ω. If E is a locally convex space, define Λ {E} as the space of all Lusinmeasurable functions f: Ω → E such that q(f(·)) is a function in Λ for every continuous seminorm q on E. The space Λ {E} is topologized in a natural way and we study some aspects of the locally convex structure of A {E}; namely, bounded sets, completeness, duality and barrelledness. In particular, we focus on the important case when Λ and E are both either metrizable or (DF)-spaces and derive good permanence results for reflexivity when the density condition holds |
Citation | Florencio Lora, M., Mayoral Masa, F. y Paúl Escolano, P.J. (2010). Dieudonné-Köthe duality for vector-valued function spaces: localization of bounded sets and barrelledness. Quaestiones Mathematicae, 20 (2), 185-214. |
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