Integral operators on the section space of a Banach bundle

doi:10.1155/S0161171293000560

International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 449-458
http://dx.doi.org/10.1155/S0161171293000560

Integral operators on the section space of a Banach bundle

J. W. kitchen ¹ and D. A. Robbins ²

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 Hindawi Publishing Corporation. 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.