Around Operator Monotone Functions

Details Around Operator Monotone Functions Around Operator Monotone Functions

2011-10-30

arxiv.org/abs/1110.6594v1

Integral Equations Operator Theory 71 (2011), no. 4, 575-582

Mathematics

Functional Analysis

9 pages; to appear in Integral Equations Operator Theory (IEOT)

Scientific paper

We show that the symmetrized product $AB+BA$ of two positive operators $A$ and $B$ is positive if and only if $f(A+B)\leq f(A)+f(B)$ for all non-negative operator monotone functions $f$ on $[0,\infty)$ and deduce an operator inequality. We also give a necessary and sufficient condition for that the composition $f\circ g$ of an operator convex function $f$ on $[0,\infty)$ and a non-negative operator monotone function $g$ on an interval $(a,b)$ is operator monotone and give some applications.

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