ISOMETRIC EMBEDDINGS OF BANACH BUNDLES

We show in this paper that every bijective linear isometry between the continuous section spaces of two non-square Banach bundles gives rise to a Banach bundle isomorphism. This is to support our expectation that the geometric structure of the continuous section space of a Banach bundle determines c...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 15; no. 5; pp. 1969 - 1978
Main Authors Hsu, Ming-Hsiu, Wong, Ngai-Ching
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.10.2011
Subjects
Banach space
Continuous functions
Hausdorff spaces
Homeomorphism
Infinity
Linear transformations
Mathematical theorems
Mathematical vectors
Sine function
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ISSN1027-5487
2224-6851
DOI10.11650/twjm/1500406417

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Summary:We show in this paper that every bijective linear isometry between the continuous section spaces of two non-square Banach bundles gives rise to a Banach bundle isomorphism. This is to support our expectation that the geometric structure of the continuous section space of a Banach bundle determines completely its bundle structures. We also describe the structure of anintoisometry from a continuous section space into an other. However, we demonstrate by an example that a non-surjective linear isometry can be far away from a subbundle embedding. 2010Mathematics Subject Classification: 46B40, 46E40, 46M20. Key words and phrases: Isometries, Banach bundles, Bundle isomorphisms, Banach-Stone type theorems.
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500406417