Properties of Toeplitz Operators on the Dirichlet Space Over the Ball |
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Authors: | Hu Yin Yin Lu Yu Feng Liu Liu |
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Institution: | 1. Department of Mathematics, Dalian Maritime University, Dalian 116024, P. R. China;2. Department of Mathematics, Dalian University of Technology, Dalian 116024, P. R. China |
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Abstract: | On the Dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the Dirichlet space and their analogues defined on the Hardy space. Based on this, we characterize when finite sums of products of Toeplitz operators are of finite rank. Also, we give a necessary and sufficient condition for the commutator and semi-commutator of two Toeplitz operators being zero. |
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Keywords: | Toeplitz operator pluriharmonic symbols Dirichlet space |
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