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Integral identities of norms and characterization of inner product spaces

Authors: Časlav V. Stanojević and Ana M. Suchanek
Journal: Proc. Amer. Math. Soc. 81 (1981), 101-103
MSC: Primary 46C05
MathSciNet review: 589146
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Abstract: Integral identities of norms over compact groups are used to characterize inner product spaces. These integral identities also generalize the Penico-Stanojević [1] integral form of the parallelogram law.

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

  • [1] A. J. Penico and Č. V. Stanojević, An integral analogue to parallelogram law, Proc. Amer. Math. Soc. 79 (1980), 427-430. MR 567985 (81j:46027)
  • [2] I. J. Schoenberg, A remark on M. M. Day's characterization of inner-product spaces and a conjecture of L. M. Blumenthal, Proc. Amer. Math. Soc. 3 (1952), 361-364.
  • [3] M. M. Day, Some characterizations of inner-product spaces, Trans. Amer. Math. Soc. 82 (1947), 320-337. MR 0022312 (9:192c)
  • [4] A. Dvoretzky and C. A. Rogers, Absolute and conditional convergence in normed linear spaces, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 192-197. MR 0033975 (11:525a)

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Keywords: Inner product spaces
Article copyright: © Copyright 1981 American Mathematical Society

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