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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Vydané v:Topology and its applications Ročník 227; s. 118 - 134
Hlavný autor: Kawamura, Kazuhiro
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 15.08.2017
Predmet:
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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Shrnutí: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