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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Veröffentlicht in:Topology and its applications Jg. 227; S. 118 - 134
1. Verfasser: Kawamura, Kazuhiro
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 15.08.2017
Schlagworte:
Banach space bundle
Isometry
Weighted composition operator
46E15
55R25
Isometry
Weighted composition operator
Banach space bundle
ISSN:0166-8641, 1879-3207
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Zusammenfassung: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