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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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 |
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doaj-6e6dfdeafa9546b4a61a401f0ff34d232020-11-24T23:49:39ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01291056357210.1155/S0161171202008086Some extremal properties of section spaces of Banach bundles and their dualsD. A. Robbins0Department of Mathematics, Trinity College, Hartford 06106, CT, USAWhen 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.http://dx.doi.org/10.1155/S0161171202008086 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
D. A. Robbins |
| spellingShingle |
D. A. Robbins Some extremal properties of section spaces of Banach bundles and their duals International Journal of Mathematics and Mathematical Sciences |
| author_facet |
D. A. Robbins |
| author_sort |
D. A. Robbins |
| title |
Some extremal properties of section spaces of Banach bundles and their duals |
| title_short |
Some extremal properties of section spaces of Banach bundles and their duals |
| title_full |
Some extremal properties of section spaces of Banach bundles and their duals |
| title_fullStr |
Some extremal properties of section spaces of Banach bundles and their duals |
| title_full_unstemmed |
Some extremal properties of section spaces of Banach bundles and their duals |
| title_sort |
some extremal properties of section spaces of banach bundles and their duals |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2002-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/S0161171202008086 |
| work_keys_str_mv |
AT darobbins someextremalpropertiesofsectionspacesofbanachbundlesandtheirduals |
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