On the monotonicity of weighted power means of matrices

Raluca Dumitru, Jose Franco

Let ${\mu }_p(A,B,t)=(t{A}^p+(1-t)B^p{)}^{1/p}$ denote the weighted power mean between positive operators $A$ and $B$. We show that the function $t\to \Vert A-{\mu }_p(A,B,t){\Vert }_2$ is monotonically d…