Properties of Toeplitz Operators on the Dirichlet Space Over the Ball
Properties of Toeplitz Operators on the Dirichlet Space Over the Ball
复制标题
球上狄利克雷空间上托普利茨算子的性质
DOI：
10.1007/s10114-019-8437-y
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发表时间：
2019
影响因子：
0.7
通讯作者：
Liu Liu
中科院分区：
文献类型：
--
作者：
Hu Yin Yin;Lu Yu Feng;Liu Liu
在单位球的Dirichlet空间上，研究了Toeplitz算子的一些代数性质.本文给出了Dirichlet空间上的Toeplitz算子与哈代空间上的Toeplitz算子之间的关系。在此基础上，我们刻画了Toeplitz算子乘积的有限和是有限秩的。同时，给出了两个Toeplitz算子的交换子和半交换子为零的充要条件。
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.