Internal functionals and bundle duals

Joseph W. Kitchen and David A. Robbins

International Journal of Mathematics and Mathematical Sciences, 1984, vol. 7, 1-7

Abstract:

If π : E → X is a bundle of Banach spaces, X compact Hausdorff, a fibered space π * : E * → X can be constructed whose stalks are the duals of the stalks of the given bundle and whose sections can be identified with the functionals studied by Seda in [1] and [2] or elements of the internal dual Mod ( Γ ( π ) , C ( X ) ) studied by Gierz in [3]. If the given bundle is separable and norm continuous, then the fibered space π * : E * → X is actually a full bundle of locally convex topological vector spaces (Theorem 3). In the second portion of the paper two results are stated, both of them corollaries of theorems by Gierz, concerning functionals for bundles of Banach spaces which arise, in turn, from fields of topological spaces.

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:170125

DOI: 10.1155/S0161171284000715

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