A characterization of nuclear operators on spaces of vector-valued continuous functions with the strict topology

Let X X be a completely regular Hausdorff space, let E E and F F denote Banach spaces. Let C b ( X , E ) C_b(X,E) denote the space of E E -valued bounded continuous functions on X X and let β β be the strict topology on this space. We establish the relationship between nuclear operators T : C b ( X , E ) → F T:C_b(X,E)→ F between the locally convex space ( C b ( X , E ) , β ) (C_b(X,E),β ) and the Banach space F F and their representing operator-valued Borel measures.