Advances in Operator Theory and Inequalities

Identifying the isometries on a normed linear space is one of the fundamental goals in functional analysis and operator theory. The classical Blanco–Koldobsky–Turn\v{s}ek theorem characterizes the isometries as the norm-one linear operators that preserve Birkhoff–James orthogonality. In this study, we consider the local preservation of Birkhoff–James orthogonality by linear operators between normed linear spaces, both at a point and in a particular direction. We obtain a complete characterization of the same, refine earlier results, and apply these findings to the identification of isometries on polyhedral Banach spaces. In particular, we present refinements of the Blanco–Koldobsky–Turn\v{s}ek theorem for certain polyhedral Banach spaces.