Nuclear operators on the space Crc(X,E) of vector-valued continuous functions

Let X be a completely regular Hausdorff space and E and F be Banach spaces. Let Crc(X,E) denote the Banach space of all continuous functions f:X→ E such that f(X) is a relatively compact set in E . Let βσ be the strict topology on Crc(X,E) . We characterize the nuclearity of a (βσ, \|·\|F) -continuous operator T:Crc(X,E)→ F in terms of its representing operator-valued Baire measure. As an application, we establish the relationship between the nuclearity of a (βσ,\|·\|F) -continuous operator T:Crc(X,E)→ F and the nuclearity of its conjugate operator T' .