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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Inner products characterized by difference equations
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by Gordon G. Johnson PDF
Proc. Amer. Math. Soc. 37 (1973), 535-536 Request permission

Abstract:

A normed linear space $X$ is an inner product space iff, for some integer $k \geqq 3$, $\sum _{t = 0}^k \binom {k}{t} (-1)^t \left \| a + ab \right \|^2 = 0$ for all $a$ and $b$ in $X$.
References
    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
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 37 (1973), 535-536
  • MSC: Primary 46C05
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0312223-4
  • MathSciNet review: 0312223