International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 10, Pages 563-572

Some extremal properties of section spaces of Banach bundles and their duals

D. A. Robbins

Department of Mathematics, Trinity College, Hartford 06106, CT, USA

Received 24 August 2001

Copyright © 2002 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.


When X is a compact Hausdorff space and E is a real Banach space there is a considerable literature on extremal properties of the space C(X,E) of continuous E-valued functions on X. What happens if the Banach spaces in which the functions on X take their values vary over X? In this paper, we obtain some extremal results on the section space Γ(π) and its dual Γ(π)* of a real Banach bundle π:X (with possibly varying fibers), and point out the difficulties in arriving at totally satisfactory results.