3 problems

Factor-valued pinching conjecture. If $A\in{\mathfrak{R}}$ satisfies $W_e^{\mathfrak{R}}(A)\supset{\mathcal{D}}$ and $\{X_i\}_{i=1}^{\infty}\subset{\mathfrak{R}}$ satisfies…

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 $0<m\le A\le M$, and let $X,Y$ be partial isometries on a Hilbert space $\mathcal{H}$ whose final spaces are orthogonal to each other. Let $\Phi$ be a $2$-positive linear map.…