On approximate preservation of orthogonality and its application to isometries

2025/01/18 by Kalidas Mandal, Mandal, Kalidas, Jayanta Manna +5 · 1 citation
Computer Science · Engineering · Mathematics · #46B04 #46B20 #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2501.10719

openalex publication_date 2025/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by the famous Blanco-Koldobsky-Turnšek characterization of isometries, we study the 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-Turnšek characterization of isometries on certain Banach spaces.

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