Hyponormal Toeplitz Operators on the Weighted Bergman Space

摘要

Consider phi-f+(g)over bar,where f and g are polynomials,and let T-phi be the Toeplitz operators with the symbol phi.It is known that if T-phi is hyponormal then vertical bar f'(z)broken vertical bar(2)>= vertical bar g'(z)vertical bar(2)on the unit circle in the complex plane.In this paper,we show that it is also a necessary and sufficient condition under certain assumptions.Furthermore,we present some necessary conditions for the hyponormality of T-phi on the weighted Bergman space,which generalize the results of I.S.Hwang and J.Lee.