On norm inequalities related to the geometric mean

Shaima'a Freewan, Mostafa Hayajneh

Let $A_i$ and $B_i$ be positive definite matrices for all $i=1,\cdots ,m.$ It is shown that $$\left|\left|\sum_{i=1}^m(A_i^2\sharp B_i^2)^r\right|\right|_1\leq\left|\left|\left(\lef…