Isometric embeddings of Banach bundles
Functional Analysis
2014-02-27 v1
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.
Keywords
Cite
@article{arxiv.1402.6426,
title = {Isometric embeddings of Banach bundles},
author = {Ming-Hsiu Hsu and Ngai-Ching Wong},
journal= {arXiv preprint arXiv:1402.6426},
year = {2014}
}