On a property of Toeplitz operators on Bergman space with a logarithmic weight

Abstract

An operator T on a Hilbert space is hyponormal if T*T-TT* is positive. In this work we consider hyponormality of Toeplitz operators on the Bergman space with a logarithmic weight. Under a smoothness assumption we give a necessary condition when the symbol is of the form $$f+\overline{g}$$ with f, g analytic on the unit disk. We also find a sufficient condition when f is a monomial and g a polynomial.