Let φ{symbol}be 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 ...
We study the inequality Tr(w(A)f(A)) ≤ Tr(w(A)f(B)), where w : ℝ → ℝ+ is a "weight function" and A, B are Hermitian matrices with A ≤ B, and find corresponding characterizations of the trace.