2 problems

Let $\Phi$ be a unital positive linear map, and let $A$ and $B$ be positive operators satisfying … and … for positive real numbers $m_{1}\leq M_{1}$ and $m_{2}\leq M_{2}$. Write…

Let $A$ and $B$ be positive operators and let $q\in\mathbb{R}$. Complementary McCarthy conjecture. … for $-2<q<0$, while the reversed inequality should hold for $3\leq q$. The disp…