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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1978-0495846-6
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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0495846-6
Keywords: Inner product space, Hilbert space, metric projection
Article copyright: © Copyright 1978 American Mathematical Society