Internal functionals and bundle duals
type: Item
instance of: scholarly article
title: Internal functionals and bundle duals
zbMATH Open document ID: 0599.46088
DOI: 10.1155/S0161171284000715
author: Joseph W. Kitchen
author: D. A. Robbins
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46100
review text: If \(\pi\) :E\(\to X\) is a bundle of Banach spaces, X compact Hausdorff, a fibered space \(\pi^*:E^*\to X\) 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 or elements of the ''internal dual'' Mod(\(\Gamma\) (\(\pi)\),C(X)) studied by Gierz. If the given bundle is separable and norm continuous, then the fibered space \(\pi^*:E^*\to X\) 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.''
Mathematics Subject Classification ID: 46M20
Mathematics Subject Classification ID: 46H25
Mathematics Subject Classification ID: 55R65
zbMATH DE Number: 3967138
zbMATH Keywords: fields of topological spaces
zbMATH Keywords: internal functions
zbMATH Keywords: bundle of Banach spaces
zbMATH Keywords: fibered space
zbMATH Keywords: stalks
zbMATH Keywords: internal dual
MaRDI profile type: Publication
OpenAlex ID: W2005111730
description: scientific article; zbMATH DE number 3967138