Topological properties of some spaces of continuous operators
Journal Title: Discussiones Mathematicae Differential Inclusions Control and Optimization - Year 2016, Vol 36, Issue 1
Abstract
Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let Cb(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 Lβ(Cb(X,E),F) of all (β,||•||F)-continuous linear operators from Cb(X,E) to F, equipped with the topology τs of simple convergence. If X is a locally compact paracompact space (resp. a P-space), we characterize τs-compact subsets of Lβ(Cb(X,E),F) in terms of properties of the corresponding sets of the representing operator-valued Borel measures. It is shown that the space ( Lβ(Cb(X,E),F), τs) is sequentially complete if X is a locally compact paracompact space.
Authors and Affiliations
Marian Nowak
Keywords
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