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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Inner products characterized by difference equations


Author: Gordon G. Johnson
Journal: Proc. Amer. Math. Soc. 37 (1973), 535-536
MSC: Primary 46C05
MathSciNet review: 0312223
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Abstract: A normed linear space X is an inner product space iff, for some integer $ k \geqq 3,\sum _{t = 0}^k(\mathop t\limits^k ){( - 1)^t}{\left\Vert {a + ab} \right\Vert^2} = 0$ for all a and b in X.


References [Enhancements On Off] (What's this?)

  • [M] M. Day, Normed linear spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, N.F., Heft 21, Academic Press, New York; Springer-Verlag, Berlin, 1962. MR 26 #2847.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0312223-4
PII: S 0002-9939(1973)0312223-4
Article copyright: © Copyright 1973 American Mathematical Society