Geodesic
Topological properties of some spaces of continuous operators
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 36 (2016) no. 1, pp. 79-86

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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.
Keywords: spaces of vector-valued continuous functions, strict topologies, operator measures, topology of simple convergence, continuous operators 
Nowak, Marian. Topological properties of some spaces of continuous operators. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 36 (2016) no. 1, pp. 79-86. http://geodesic.mathdoc.fr/item/DMDICO_2016_36_1_a4/
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