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Proceedings of the American Mathematical Society

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

 

 

A characterization of Hilbert space


Author: Ronald E. Bruck
Journal: Proc. Amer. Math. Soc. 43 (1974), 173-175
MSC: Primary 46C05
DOI: https://doi.org/10.1090/S0002-9939-1974-0341038-7
MathSciNet review: 0341038
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Abstract: A real Banach space $ E$ of dimension $ \geqq 3$ is an inner product space iff there exists a bounded smooth convex subset of $ E$ which is the range of a nonexpansive retraction.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0341038-7
Keywords: Nonexpansive retract
Article copyright: © Copyright 1974 American Mathematical Society