Characterization of inner product spaces by unitary Carlsson type orthogonalities

Abstract

In this study, we consider the Hermite-Hadamard type of unitary Carlsson?s orthogonality (UHH-C-orthogonality) to characterize real inner product spaces. We give a necessary and sufficient condition weaker than the homogeneity of symmetric HH-C-orthogonalities which characterizes inner product spaces among normed linear spaces of dimension at least three. In conclusion, some more characterizations of real inner product spaces are provided.