Pullbacks of Banach bundles
type: Item
instance of: scholarly article
title: Pullbacks of Banach bundles
zbMATH Open document ID: 0762.46050
published in: Rocky Mountain Journal of Mathematics
publication date: 1993-01-17T00:00:00Z
review text: Le résultat principal peut s'énoncer ainsi: \(S\) et \(T\) sont deux espaces compacts, \(\alpha: S\to T\) une application continue, \(\varphi: F\to T\) un fibré de Banach, \(\pi: E\to S\) son obstruction par \(\alpha\), \(K\) l'enveloppe linéaire fermée dans \(C(S)\widehat{\widehat\otimes} \Gamma(\rho)\) de l'ensemble des éléments de la forme \((g\cdot f)\otimes \sigma-f\otimes(g\sigma)\) [où \(g\), \(f\), \(\sigma\) appartiennent à \(C(T)\), \(C(S)\), \(\Gamma(\rho)\)]; il existe un isomorphisme isométrique \(\varphi\) entre \(C(S)\widehat{\widehat\otimes} \Gamma(\rho))/K\) et \(\Gamma(\pi)\); on a, en outre, \(\varphi(f\otimes\sigma+K)= f(\sigma\circ\alpha)\).
Mathematics Subject Classification ID: 46H25
Mathematics Subject Classification ID: 46M05
zbMATH DE Number: 97434
zbMATH Keywords: pullbacks of Banach bundles
author: Joseph W. Kitchen
author: D. A. Robbins
reviewed by: Henri Mascart
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072757
OpenAlex ID: W1981030205
cites work: Bundles of topological vector spaces and their duality
cites work: Tensor products of Banach bundles
cites work: Q3333573
cites work: Sectional representations of Banach modules
cites work: Internal functionals and bundle duals
cites work: Linear algebra in the category of C(X)-locally convex modules
cites work: Induced Banach representations of Banach algebras and locally compact groups
cites work: Banach Bundles of Continuous Functions and an Integral Representation Theorem
DOI: 10.1216/RMJM/1181072757
description: scientific article; zbMATH DE number 97434