On Birkhoff-James orthogonality preservers between real non-isometric Banach spaces
Functional Analysis
2021-08-03 v1
Abstract
Real smooth three-dimensional or higher Banach spaces are isomorphic with respect to the nonlinear structure of Birkhoff-James orthogonality if and only if they are isometrically isomorphic. Moreover, using smooth Radon planes and non-smooth direct sums, in arbitrary dimensions, we construct examples of non-isometric pairs of real Banach spaces that admit norm-preserving homogeneous bicontinuous Birkhoff-James orthogonality preservers among them.
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Cite
@article{arxiv.2108.00655,
title = {On Birkhoff-James orthogonality preservers between real non-isometric Banach spaces},
author = {Ryotaro Tanaka},
journal= {arXiv preprint arXiv:2108.00655},
year = {2021}
}
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13 pages