Integral Equations and Operator Theory

, Volume 65, Issue 1, pp 115–129 | Cite as

Hyponormal Toeplitz Operators on the Weighted Bergman Space

Article

Abstract.

Consider \(\varphi = f + \overline {g}\), where f and g are polynomials, and let \(T_{\varphi}\) be the Toeplitz operators with the symbol \(\varphi\). It is known that if \(T_{\varphi}\) is hyponormal then \(|f'(z)|^{2} \geq |g'(z)|^{2}\) 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 \(T_{\varphi}\) on the weighted Bergman space, which generalize the results of I. S. Hwang and J. Lee.

Mathematics Subject Classification (2000).

Primary 47B35 Secondary 47B20 

Keywords.

Hyponormality weighted Bergman space Hankel operator Toeplitz operator 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.School of Mathematical SciencesDalian University of TechnologyDalianChina

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