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

D. A. Robbins

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 29, 1-10

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.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:521715

DOI: 10.1155/S0161171202008086

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