Affiliation:
1. Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Ulica Szafrana 4A, 65-516 Zielona Góra, Poland
Abstract
LetXbe a completely regular Hausdorff space, and let(E,‖·‖E)and(F,‖·‖F)be Banach spaces. LetCb(X,E)be the space of allE-valued bounded, continuous functions defined onX, equipped with the strict topologiesβz, where z=σ,∞,p,τ,t. General integral representation theorems of(βz,‖·‖F)-continuous linear operators T:Cb(X,E)→F with respect to the corresponding operator-valued measures are established. Strongly bounded and(βz,‖·‖F)-continuous operatorsT:Cb(X,E)→Fare studied. We extend to “the completely regular setting” some classical results concerning operators on the spacesC(X,E)andCo(X,E), whereX is a compact or a locally compact space.