On hyponormality on a weighted annulus

Abstract

In this work, we consider the hyponormality of Toeplitz operators on the Bergman space of the annulus with a logarithmic weight. We give necessary conditions when the symbol is of the form φ+ψ¯\varphi +\overline{\psi }, where φ\varphi and ψ\psi are analytic on the annulus {z∈C;1/2<∣z∣<1}\{z\in {\mathbb{C}};\hspace{0.25em}1\hspace{-0.08em}\text{/}\hspace{-0.08em}2\lt | z| \lt 1\}.

Keywords

• toeplitz operator
• weighted bergman spaces
• hyponormality
• positive matrices
• 47b35
• 47b20
• 15b48