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Jordan triple mappings on positive definite matrices

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Abstract

The main aim of this paper is to characterize the determinant function on the set of positive definite \({n \times n}\) matrices with entries from \({{\mathbb{F}}}\).

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References

  1. Aczél J.: Lectures on Functional Equations and their Applications, pp. XIX 510. Academic Press, New York and London (1966)

    MATH  Google Scholar 

  2. Bhatia, R.: Positive definite matrices. In: Princeton Series in Applied Mathematics. Princeton University Press, Princeton (2007)

  3. Bobecka K., Wesołowski J.: Multiplicative Cauchy functional equation in the cone of positive-definite symmetric matrices. Ann. Polon. Math. 82(1), 1–7 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dobovišek M.: Maps from \({M_n(\mathbb{F})}\) to \({\mathbb{F}}\) that are multiplicative with respect to the Jordan triple product. Publ. Math. Debrecen 73(1-2), 89–100 (2008)

    MATH  MathSciNet  Google Scholar 

  5. Fearnley-Sander D.: A characterization of the determinant. Am. Math. Monthly 82(8), 838–840 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gáspár G.: Die Charakterisierung der Determinanten über einem unendlichen Integritätsbereich mittels Funktionalgleichungen. Publ. Math. Debrecen 10, 244–253 (1963)

    MathSciNet  Google Scholar 

  7. Hitotumatu S.: A characterization of the determinant. Comment. Math. Univ. St. Paul. 13, 45–50 (1964/1965)

    MATH  MathSciNet  Google Scholar 

  8. Kuczma, M.: An introduction to the theory of functional equations and inequalities. In: Gilányi, A. (ed.) Cauchy’s Equation and Jensen’s Inequality, 2nd edn. Birkhäuser, Basel, xiv, 595 p (2009)

  9. Kurepa S.: On the characterization of the determinant. Glasnik Mat-Fiz. Astronom. Ser. II Društvo Mat. Fiz. Hrvatske 19, 189–198 (1964)

    MATH  MathSciNet  Google Scholar 

  10. McDonald B.R.: A characterization of the determinant. Linear Multilinear Algebra 12(1), 31–36 (1982/83)

    Article  Google Scholar 

  11. Molnár, L.: A remark on the Kochen-Specker theorem and some characterizations of the determinant on sets of Hermitian matrices. Proc. Am. Math. Soc. 134(10) 2839–2848 (2006) (electronic)

    Google Scholar 

  12. Yamaguti K.: Jordan and Jordan triple isomorphisms of rings. J. Sci. Hiroshima Univ. Ser. A 20, 107–110 (1956)

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. MTA-DE ‘Lendület’, Functional Analysis Research Group, Institute of Mathematics, University of Debrecen, P. O. Box 12, Debrecen, 4010, Hungary

    Eszter Gselmann

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  1. Eszter Gselmann
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Correspondence to Eszter Gselmann.

Additional information

This research has been supported by the Hungarian Scientific Research Fund (OTKA) Grant NK 814 02 and by the ’Lendület’ Program (LP2012-46/2012) of the Hungarian Academy of Sciences.

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Gselmann, E. Jordan triple mappings on positive definite matrices. Aequat. Math. 89, 629–639 (2015). https://doi.org/10.1007/s00010-013-0251-5

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  • DOI: https://doi.org/10.1007/s00010-013-0251-5

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