On approximate preservation of orthogonality and its application to isometries

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.