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Weak n-inner product spaces

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Abstract

In this article, we study a generalization of the n-inner product which we name weak n-inner product. As particular case, we consider the n-iterated 2-inner product and we give its representation in terms of the standard k-inner products, \(k\le n\), using the Dodgson’s identity for determinants. Finally, we present several applications, including a brief characterization of a linear regression model for the random variables in discrete case and a generalization of the Chebyshev functional using the n-iterated 2-inner product.

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Acknowledgements

The authors would like to thank to the reviewers for the pertinent remarks, which led to an improvement of the paper.

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Authors and Affiliations

  1. Transilvania University of Braşov, Iuliu Maniu 50, 500091, Braşov, Romania

    Nicuşor Minculete & Radu Păltănea

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  1. Nicuşor Minculete
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  2. Radu Păltănea
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Correspondence to Radu Păltănea.

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Communicated by Jacek Chmielinski.

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Minculete, N., Păltănea, R. Weak n-inner product spaces. Ann. Funct. Anal. 12, 22 (2021). https://doi.org/10.1007/s43034-020-00108-3

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