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arXiv · 2108.00655

On Birkhoff-James orthogonality preservers between real non-isometric Banach spaces

Ryotaro Tanaka
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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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Ryotaro Tanaka. 2021-08-02. On Birkhoff-James orthogonality preservers between real non-isometric Banach spaces. https://arxiv.org/abs/2108.00655

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