Characterization of the trace by monotonicity inequalities

摘要

Let phi be a positive linear functional on the algebra of n x 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 x n matrices with A <= B the inequality phi(A(p)) <= phi(B-P) holds true, then phi is a nonnegative scalar multiple of the trace. (c) 2006 Elsevier Inc. All rights reserved.