Characterization of the trace by monotonicity inequalities Original Research Article

Let phibe a positive linear functional on the algebra of n × n complex matrices and p be a number greater than 1. The main result of the paper says that if for any pair A, B of positive semi-definite n × n matrices with A less-than-or-equals, slant B the inequality phi(Ap) less-than-or-equals, slant phi(Bp) holds true, then phiis a nonnegative scalar multiple of the trace.