International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 449-458
doi:10.1155/S0161171293000560
Integral operators on the section space of a Banach bundle
J.W. Kitchen1
and D.A. Robbins2
1Department of Mathematics, Duke University, Durham 27706, NC, USA
2Department of Mathematics, Trinity College, Hartford 06106, CT, USA
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.