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 characterize‎‎real inner product spaces‎. ‎We give a necessary and sufficient condition weaker than the homogeneity of symmetric HH-C-orthogonalities in real normed linear space X with dimension at least 3‎, ‎that under which the norm of X comes from an inner product‎. ‎In conclusion‎, ‎some more characterizations of real inner product spaces are provided‎.