On approximate preservation of orthogonality and its application to isometries

Motivated by the famous Blanco-Koldobsky-Turnšek characterization of isometries, we study the $\mathit{\text{approximate}}\mathit{\text{preservation}}\mathit{\text{of}}\mathit{\text{Birkhoff-James}}\mathit{\text{orthogonality}}\mathit{\text{by}}\mathit{\text{a}}\mathit{\text{linear}}\mathit{\text{operator}}\mathit{\text{between}}\mathit{\text{Banach}}\mathit{\text{spaces}}$. 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.