New characterizations of operator monotone functions

Trung Hoa Dinh, Raluca Dumitru, Jose Franco

If $\sigma$ is a symmetric mean and $f$ is an operator monotone function on $[0,\infty )$, then $$f(2(A^{-1}+B^{-1}{)}^{-1})\le f(A\sigma B)\le f((A+B)/2).$$ Conversely, Ando and Hiai showed th…