‎The aim of this paper is to find some sufficient conditions for positivity of block matrices of positive operators‎. ‎It is shown that for positive operators $A,B,C$ and for every non-negative operator monotone function $f$ on $‎ ‎(0,\infty)$‎, ‎the block matrix‎ ‎\begin{align*}‎ ‎\left(‎ ‎\begin{array}{cc}‎ ‎f(A) & f(C) \\‎ ‎f(C) & f(B) \\‎ ‎\end{array}‎ ‎\right)‎ ‎\end{align*}‎ ‎is positive if and only if $C \leq A!B$‎. ‎In particular‎, ‎if $C \leq A!B$ then‎ ‎\begin{equation*}‎ ‎\left(‎ ‎\begin{array}{cc}‎ ‎A & C \\‎ ‎C & B \\‎ ‎\end{array}‎ ‎\right)‎, ‎\end{equation*}‎ ‎is positive‎.

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