Abstract
It is well known that the property of additivity of pythagorean orthogonality characterizes real inner product spaces among normed linear spaces. In the present paper, a natural concept of additivity is introduced in metric spaces, and it is shown that a weakened version of this additivity of metric pythagorean orthogonality characterizes real inner product spaces among complete, convex, externally convex metric spaces, providing a generalization of the earlier characterization.
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References
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Freese, R., Andalafte, E. Weak additivity of metric pythagorean orthogonality. J Geom 54, 44–49 (1995). https://doi.org/10.1007/BF01222851
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DOI: https://doi.org/10.1007/BF01222851