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 condi-
tion 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