Integral identities of norms and characterization of inner product spaces
HTML articles powered by AMS MathViewer
- by Časlav V. Stanojević and Ana M. Suchanek PDF
- Proc. Amer. Math. Soc. 81 (1981), 101-103 Request permission
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
- A. J. Penico and Č. V. Stanojević, An integral analogue to parallelogram law, Proc. Amer. Math. Soc. 79 (1980), no. 3, 427–430. MR 567985, DOI 10.1090/S0002-9939-1980-0567985-1 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.
- Mahlon M. Day, Some characterizations of inner-product spaces, Trans. Amer. Math. Soc. 62 (1947), 320–337. MR 22312, DOI 10.1090/S0002-9947-1947-0022312-9
- A. Dvoretzky and C. A. Rogers, Absolute and unconditional convergence in normed linear spaces, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 192–197. MR 33975, DOI 10.1073/pnas.36.3.192
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 101-103
- MSC: Primary 46C05
- DOI: https://doi.org/10.1090/S0002-9939-1981-0589146-3
- MathSciNet review: 589146