4 problems

Power hyponormality conjecture. If

The conjecture. In Sector II, except on its boundary with Sector I, no $\alpha$ is interpolated by a Bernstein function; in Sector III, $W_\alpha$ is subnormal, and except on its b…

For $0 \le t \le \frac{1}{2}$, the generalized mean transform of a linear operator $T$ is defined by … where $\widetilde{T}(t):=|T|^tU|T|^{1-t}$ is the generalized Aluthge transfor…

A-F-M conjecture. The multiplication operator $M_z$ on $\mathcal H(K_1+K_2)$ is subnormal.