Inequalities for Determinants and Characterization of the Trace

Abstract

© 2020, Pleiades Publishing, Ltd. Let tr be the canonical trace on the full matrix algebra ℳn 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 ℳn 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.