Marian Nowak
(2016)

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 ${L}_{\beta}({C}_{b}(X,E),F)$ of all $(\beta ,|\left|\xb7\right|{|}_{F})$-continuous linear operators from ${C}_{b}(X,E)$ to F, equipped with the topology ${\tau}_{s}$ of simple convergence. If X is a locally compact paracompact space (resp. a P-space), we characterize ${\tau}_{s}$-compact subsets of ${L}_{\beta}({C}_{b}(X,E),F)$ in terms of properties of the corresponding sets of the representing...