English

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.

Keywords

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