Hyponormality on a Weighted Bergman Space

摘要

A bounded Hilbert space operator T is hyponormal if T?T?TT? 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+gˉ where f and g are bounded analytic functions on the unit disk. We then find sufficient conditions when f is a monomial.