Topological properties of some spaces of continuous operators

Marian Nowak

Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 36 (2016), p. 79-86 / Harvested from The Polish Digital Mathematics Library

Résumé

Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let $C_b(X,E)$ be the space of all E-valued bounded continuous functions on X, equipped with the strict topology β. We study topological properties of the space $L_{β}(C_{b}(X,E),F)$ of all $(β,||·||_{F})$-continuous linear operators from $C_{b}(X,E)$ to F, equipped with the topology $τ_{s}$ of simple convergence. If X is a locally compact paracompact space (resp. a P-space), we characterize $τ_{s}$-compact subsets of $L_{β}(C_{b}(X,E),F)$ in terms of properties of the corresponding sets of the representing operator-valued Borel measures. It is shown that the space $(L_{β}(C_{b}(X,E),F),τ_{s})$ is sequentially complete if X is a locally compact paracompact space.

Détail

Publié le : 2016-01-01
EUDML-ID : urn:eudml:doc:286913

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