Banach–Stone theorems for spaces of vector bundle continuous sections

We prove Banach–Stone type theorems for linear isometries on spaces of continuous sections of Banach space bundles. These extend a previous result for vector-valued continuous function spaces. Two common methods, examining the extreme point sets of the dual spaces and examining peak points, are adop...

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Bibliographic Details
Published in:Topology and its applications Vol. 227; pp. 118 - 134
Main Author: Kawamura, Kazuhiro
Format: Journal Article
Language:English
Published: Elsevier B.V 15.08.2017
Subjects:
Banach space bundle
Isometry
Weighted composition operator
46E15
55R25
Isometry
Weighted composition operator
Banach space bundle
ISSN:0166-8641, 1879-3207
Online Access:Get full text
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Summary:We prove Banach–Stone type theorems for linear isometries on spaces of continuous sections of Banach space bundles. These extend a previous result for vector-valued continuous function spaces. Two common methods, examining the extreme point sets of the dual spaces and examining peak points, are adopted to prove two similar but slightly different theorems.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2017.01.023