2 problems

Let $X$ and $Y$ be positive operators, and for $p\geq2$ define the weighted power mean $(tX^p+(1-t)Y^p)^{1/p}$ for $0\leq t\leq1$. Power-mean monotonicity conjecture. The function…

Let $A$ and $B$ be positive operators, let $t\in[0,1]$, and for $p\geq 1$ define the weighted $p$-power mean by … The results that weighted $p$-power means are distance-monotonic a…