An improvement of the Blanco-Koldobsky-Turnsek characterization of isometries
Abstract
We present an improvement of the Blanco-Koldobsky-Turnsek 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 Krein-Milman property, we derive an additional refinement of the Blanco-Koldobsky-Turnsek characterization of isometries.
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