Integral operators on spaces of continuous vector-valued functions

Abstract

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 terms of their representing vector measures. This is then used to give some applications to nuclear operators on C(X,E) spaces