## Oleg Evgen'evich Tikhonov

Dinh Trung Hoa

# 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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