An improvement of the Blanco-Koldobsky-Turnšek characterization of isometries

Abstract

We present an improvement of the Blanco-Koldobsky-Turnšek characterization of isometries in normed linear spaces by using the concept of level vectors of an operator. In this context, we characterize level vectors entirely through directional preservation of Birkhoff-James orthogonality and analyze the associated geometric and structural phenomena that they induce. Furthermore, in spaces whose unit balls possess the \textit{Krein-Milman property}, we derive an additional refinement of the Blanco-Koldobsky-Turnšek characterization of isometries.