English

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}
}