Weighted trace inequalities of monotonicity

(Lobachevskii Journal of Mathematics, Vol.25, pp.63-67 )

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.

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