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

Received 5 December 1991; Revised 15 August 1992

Copyright © 1993 J. W. kitchen and D. A. Robbins. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.