We prove that a space X is an inner product space if and only if it is true that whenever x, y are √ points in ∂B such that the line through x and y supports (2)^(1/2)/2 B then x ⊥ y in the sense of Birkhoff.
Characterizations of inner product spaces by orthogonal vectors
BARONTI, MARCO;
2006-01-01
Abstract
We prove that a space X is an inner product space if and only if it is true that whenever x, y are √ points in ∂B such that the line through x and y supports (2)^(1/2)/2 B then x ⊥ y in the sense of Birkhoff.
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