A note on intertwining $M$-hyponormal operators
A note on intertwining $M$-hyponormal operators
If $AX = X{B^ * }$ with $A$ and $B$ $M$-hyponormal, then ${A^ * }X = XB$. Furthermore, ${({\text {ran}}\;X)^ - }$ reduces $A$, ker $X$ reduces $B$, and $A|{({\text {ran}}\;X)^ - }$ and ${B^ * }|{\ker ^ \bot }X$ are unitarily equivalent normal operators. An asymptotic version is also …