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Properties of Toeplitz Operators on the Dirichlet Space Over the Ball
Yin; Yin; HU; Yu; Feng; LU; Liu; LIU Department; of; Mathematics; Dalian; Maritime; University; Dalian; 116024; P.R.China; Department; of; Mathematics; Dalian; University; of; Technology; Dalian; 116024; P.R.China
- toeplitz
- operator
- pluriharmonic
- symbols
- dirichlet
摘要：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.
- toeplitz
- operator
- pluriharmonic
- symbols
- dirichlet
摘要：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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