Algebraic Properties of Toeplitz Operators on the Polydisk

Bo Zhang, Yanyue Shi and Yufeng Lu

Abstract and Applied Analysis, 2011, vol. 2011, 1-18

Abstract:

We discuss some algebraic properties of Toeplitz operators on the Bergman space of the polydisk . Firstly, we introduce Toeplitz operators with quasihomogeneous symbols and property (P). Secondly, we study commutativity of certain quasihomogeneous Toeplitz operators and commutators of diagonal Toeplitz operators. Thirdly, we discuss finite rank semicommutators and commutators of Toeplitz operators with quasihomogeneous symbols. Finally, we solve the finite rank product problem for Toeplitz operators on the polydisk.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:962313

DOI: 10.1155/2011/962313

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