Some extremal properties of section spaces of Banach bundles and their duals
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...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202008086 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |