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 |
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Wiley
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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| author | D. A. Robbins |
| author_facet | D. A. Robbins |
| author_sort | D. A. Robbins |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-6e6dfdeafa9546b4a61a401f0ff34d23 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-6e6dfdeafa9546b4a61a401f0ff34d232025-02-03T05:51:04ZengWileyInternational 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 |
| spellingShingle | D. A. Robbins Some extremal properties of section spaces of Banach bundles and their duals International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/S0161171202008086 |
| work_keys_str_mv | AT darobbins someextremalpropertiesofsectionspacesofbanachbundlesandtheirduals |