Isometric embeddings of Banach bundles

Ming-Hsiu Hsu; Ngai-Ching Wong

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arXiv · 1402.6426

Isometric embeddings of Banach bundles

Ming-Hsiu Hsu·Ngai-Ching Wong

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Abstract

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 \emph{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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Ming-Hsiu Hsu, Ngai-Ching Wong. 2014-02-26. Isometric embeddings of Banach bundles. https://arxiv.org/abs/1402.6426

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