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Another approximation theoretic characterization of inner product spaces

Authors: Dan Amir and Frank Deutsch
Journal: Proc. Amer. Math. Soc. 71 (1978), 99-102
MSC: Primary 46C05; Secondary 41A65
MathSciNet review: 495846
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Abstract: A normed space E is an inner product space if and only if for every 2-dimensional subspace V and every segment $ I \subset V$, the corresponding metric projections satisfy the commutative property $ {P_I}{P_V} = {P_V}{P_I}$.

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Keywords: Inner product space, Hilbert space, metric projection
Article copyright: © Copyright 1978 American Mathematical Society

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