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A characterization of inner product spaces


Author: R. A. Tapia
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0341041-6
Keywords: Inner product, differentiability of the norm, Riesz representation theorem
Article copyright: © Copyright 1973 American Mathematical Society

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