On approximate preservation of orthogonality and its application to isometries
Functional Analysis
2025-01-22 v1
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.
Keywords
Cite
@article{arxiv.2501.10719,
title = {On approximate preservation of orthogonality and its application to isometries},
author = {Kalidas Mandal and Jayanta Manna and Kallol Paul and Debmalya Sain},
journal= {arXiv preprint arXiv:2501.10719},
year = {2025}
}