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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2009; 46(3): 621-642

Printed May 1, 2009

https://doi.org/10.4134/JKMS.2009.46.3.621

Copyright © The Korean Mathematical Society.

Commutativity and hyponormality of Toeplitz operators on the weighted Bergman space

Yufeng Lu and Chaomei Liu

Dalian university of Technology

Abstract

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In this paper we give necessary and sufficient conditions that two Toeplitz operators with monomial symbols acting on the weighted Bergman space commute. We also present necessary and sufficient conditions for the hyponormality of Toeplitz operators with some special symbols on the weighted Bergman space. All the results are stated in terms of the Mellin transform of the symbol.

Keywords: weighted Bergman space, Toeplitz operator, Mellin transform, commutativity, hyponormality

MSC numbers: Primary 47B35, 47B20

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