Abstract
Characterizations of real inner product spaces among normed linear spaces have been obtained by exploring properties of and relationships between various orthogonality relations which can be defined in such spaces. In the present paper the authors present metrized versions of some of these properties and relationships and obtain new characterizations of real inner product spaces among complete, convex, externally convex metric spaces.
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Freese, R., Andalafte, E. Metrizations of orthogonality and characterizations of inner product spaces. J Geom 39, 28–37 (1990). https://doi.org/10.1007/BF01222138
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DOI: https://doi.org/10.1007/BF01222138