5 problems

Curto–Muhly–Xia conjecture. The pair $\mathbf{T}$ is subnormal if and only if it is hyponormal.

Curto–Hwang–Lee conjecture. There exists a finite Blaschke–Potapov product $B\in\mathcal{E}(\Phi)$ such that

Let $W_{\mathcal A}$ be a cubically hyponormal matrix-valued weighted shift, and let $x\in\mathcal H$. Suppose that … for some $k\geq 1$. Backward propagation conjecture. Then … fo…

Let $N>4$ be a positive integer. The Cesàro matrix $C(N)$ has entries … and define the diagonal operator … Hyponormality conjecture for Cesàro matrices. The operator $C(N)$ is boun…

Let $M\in\mathcal{B}(\ell^2)$ be the generalized Cesàro matrix of order two with parameter $\alpha$. Hyponormality conjecture. The operator $M$ is also hyponormal for…