EXTREMAL PROBLEM OF A QUADRATICALLY HYPONORMAL WEIGHTED SHIFT

Let , be a recursively generated quadratically hyponormal weighted shift with a weight sequence : 1, (1, , ). In [4] Curto-Jung showed that R = {(x,y) : is quadratically hyponormal} is a closed convex with nonempty interior, which guarantees that there are a lot of quadratically hyponormal weighted shifts with first two equal weights. They suggested a problem computing expressions of certain extremal points of R. In this note we obtain a partial answer of their extremal problem.