On Hyponormality of Toeplitz Operators on the Weighted Bergman Space

Abstract

In this paper we give necessary and sufficient conditions for the hyponormality of the Toeplitz operator $T_\varphi$ on the weighted Bergman space $A^2_\alpha(\mathbb{D})$ for $\varphi(z)=\bar{a}_{-3}\bar{z}^3+\bar{a}_{-1}\bar{z}+a_1z+a_3z^3$ and $\varphi(z)=\bar{a}_{-3}\bar{z}^3+\bar{a}_{-2}\bar{z}^2+a_2z^2+a_3z^3$.