International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 10, Pages 563-572
doi:10.1155/S0161171202008086
Some extremal properties of section spaces of Banach bundles and their duals
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.
Abstract
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:ℰ→X (with possibly varying fibers), and point out the difficulties in arriving at totally satisfactory results.