On approximate preservation of orthogonality and its application to isometries
Volume 179 / 2025
Colloquium Mathematicum 179 (2025), 189-211
MSC: Primary 46B20; Secondary 46B04
DOI: 10.4064/cm9612-7-2025
Published online: 12 November 2025
Abstract
Motivated by the famous Blanco–Koldobsky–Turnšek characterization of isometries, we examine the approximate preservation of Birkhoff–James orthogonality by a linear operator defined on normed linear spaces. In particular, we investigate various geometric and analytic properties related to such preservation on finite-dimensional polyhedral Banach spaces. As a consequence, we present refinements of the Blanco–Koldobsky–Turnšek characterization of isometries on certain Banach spaces.
