Hyponormality on a Weighted Bergman Space.

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 + g ¯ where f and g are bounded analytic functions on the unit disk. We then find sufficient conditions when f is a monomial. [ABSTRACT FROM AUTHOR]