Hyponormality on a weighted Bergman space (Q2198810)

Summary: A bounded Hilbert space operator \(T\) is hyponormal if \(T^* T-T T^*\) is a positive operator. We consider the hyponormality of Toeplitz operators on a weighted Bergman space. We find a necessary condition for hyponormality in the case of a symbol of the form \(f+\overline{g}\) where \(f\) and \(g\) are bounded analytic functions on the unit disk. We then find sufficient conditions when \(f\) is a monomial.