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arXiv · 2501.10719

On approximate preservation of orthogonality and its application to isometries

Kalidas Mandal·Jayanta Manna·Kallol Paul·Debmalya Sain
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Abstract

Motivated by the famous Blanco-Koldobsky-Turn\v{s}ek characterization of isometries, we study the \textit{approximate preservation of Birkhoff-James orthogonality by a linear operator between Banach spaces}. In particular, we investigate various geometric and analytic properties related to such preservation on finite-dimensional polyhedral Banach spaces. As an application of the results obtained here, we present refinements of the Blanco-Koldobsky-Turn\v{s}ek characterization of isometries on certain Banach spaces.

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Kalidas Mandal, Jayanta Manna, Kallol Paul, Debmalya Sain. 2025-01-18. On approximate preservation of orthogonality and its application to isometries. https://arxiv.org/abs/2501.10719

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