Integral operators on the section space of a Banach bundle (Q687849)

Summary: Let \(\pi: E\to X\) and \(\rho: F\to X\) be bundles of Banach spaces, where \(X\) is a compact Hausdorff space, and let \(V\) be a Banach space. Let \(\Gamma(\pi)\) denote the space of sections of the bundle \(\pi\). We obtain two representations of integral operators \(T: \Gamma(\pi) \to V\) 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 \(T: \Gamma(\pi)\to \Gamma(\rho)\) which are \(C(X)\)-linear.