Integral Operators on Spaces of Continuous Vector-valued Functions

Let $X$ be a compact Hausdorff space, let $E$ be a Banach space, and let $C(X,E)$ stand for the Banach space of $E$-valued continuous functions on $X$ under the uniform norm. In this paper we characterize Integral operators (in the sense of Grothendieck) on $C(X,E)$ spaces in term of their representing vector measures. This is then used to give some applications to Nuclear operators on $C(X,E)$ spaces.