Isometric embeddings of Banach bundles

Ming-Hsiu Hsu Ngai-Ching Wong

Functional Analysis mathscidoc:1910.43704

Taiwanese Journal of Mathematics, 15, (5), 1969-1978, 2011
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 an into isometry 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.
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  title={Isometric embeddings of Banach bundles},
  author={Ming-Hsiu Hsu, and Ngai-Ching Wong},
  booktitle={Taiwanese Journal of Mathematics},
Ming-Hsiu Hsu, and Ngai-Ching Wong. Isometric embeddings of Banach bundles. 2011. Vol. 15. In Taiwanese Journal of Mathematics. pp.1969-1978.
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