Abstract
Let tr be the canonical trace on the full matrix algebra \({{\cal M}_n}\) with unit I. We prove that if some analog of classical inequalities for the determinant and trace (or the permanent and trace) of matrices holds for a positive functional φ on \({{\cal M}_n}\) with φ(I) = n, then φ = tr. Also, we generalize Fischer’s inequality for determinants and establish a new inequality for the trace of the matrix exponential.
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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 2, pp. 314–321.
The research was funded by the subsidy allocated to Kazan Federal University for the State Assignment in the Sphere of Scientific Activities, Project 1.13556.2019/13.1.
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Bikchentaev, A.M. Inequalities for Determinants and Characterization of the Trace. Sib Math J 61, 248–254 (2020). https://doi.org/10.1134/S0037446620020068
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DOI: https://doi.org/10.1134/S0037446620020068