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arXiv · 2407.08900

On local preservation of orthogonality and its application to isometries

Debmalya Sain·Jayanta Manna·Kallol Paul
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Abstract

We investigate the local preservation of Birkhoff-James orthogonality at a point by a linear operator on a finite-dimensional Banach space and illustrate its importance in understanding the action of the operator in terms of the geometry of the concerned spaces. In particular, it is shown that such a study is related to the preservation of k-smoothness and the extremal properties of the unit ball of a Banach space. As an application of the results obtained in this direction, we obtain a refinement of the well-known Blanco-Koldobsky-Turnsek characterization of isometries on some polyhedral Banach spaces, including $ \ell_{\infty}^n, \ell_1^n. $

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Debmalya Sain, Jayanta Manna, Kallol Paul. 2024-07-12. On local preservation of orthogonality and its application to isometries. https://doi.org/10.1016/j.laa.2024.03.004

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