On approximate preservation of orthogonality and its application to isometries
Abstract
Motivated by the famous Blanco-Koldobsky-Turnsek 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-Turnsek characterization of isometries on certain Banach spaces.
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