A characterization of inner product spaces
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- by R. A. Tapia
- Proc. Amer. Math. Soc. 41 (1973), 569-574
- DOI: https://doi.org/10.1090/S0002-9939-1973-0341041-6
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Abstract:
In this paper we define a generalized inner product on an arbitrary normed linear space and use this generalized inner product to characterize inner product spaces in the class of all normed linear spaces. We give a sharp statement of a generalized Riesz representation theorem for bounded linear functionals. This theorem should be useful in generalizing the notions of gradient methods and reproducing kernel spaces.References
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Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 569-574
- MSC: Primary 46C05; Secondary 46B05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0341041-6
- MathSciNet review: 0341041