Integral operators on the section space of a Banach bundle

Abstract

Let π:E→X and ρ:F→X be bundles of Banach spaces, where X is a compact Hausdorff space, and let V be a Banach space. Let Γ(π) denote the space of sections of the bundle π. We obtain two representations of integral operators T:Γ(π)→V in terms of measures. The first generalizes a recent result of P. Saab, the second generalizes a theorem of Grothendieck. We also study integral operators T:Γ(π)→Γ(ρ) which are C(X)-linear.