Hyponormality of Toeplitz operators on the Bergman space

In Sung Hwang

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J. Korean Math. Soc. 2008; 45(4): 1027-1041

Printed July 1, 2008

Hyponormality of Toeplitz operators on the Bergman space

In Sung Hwang

Sungkyunkwan University

Abstract

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Abstract

In this paper we consider the hyponormality of Toeplitz operators $T_{\varphi}$ on the Bergman space $L_a^2(\Bbb D)$ in the cases, where $\varphi:=f+ \overline{g}$ ($f$ and $g$ are polynomials). We present some necessary or sufficient conditions for the hyponormality of $T_\varphi$ under certain assumptions about the coefficients of $\varphi$.

Keywords: Toeplitz operators, hyponormal operators, Bergman space

MSC numbers: Primary 47B20, 47B35