The commutant and similarity invariant of analytic Toeplitz operators on Bergman space
The commutant and similarity invariant of analytic Toeplitz operators on Bergman space
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DOI：
10.1007/s11425-007-0027-2
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发表时间：
2007-05
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影响因子：
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通讯作者：
Chunlan Jiang;Yu-cheng Li
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文献类型：
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作者：
Chunlan Jiang;Yu-cheng Li
著名的vonNeumann-Wold定理告诉我们，每一个具有n + 1-Blaschke因子的解析Toeplitz算子都是哈代空间上单侧移位的酉ton+ 1个拷贝.显然，冯诺伊曼-沃尔德定理在伯格曼空间中不成立。本文利用Michael和Zhu在Bergman空间上构造的基，证明了每个解析Toeplitz算子MB（z）相似于Bergman移位的ton+ 1个拷贝当且仅当B（z）是ann+ 1-Blaschke积.从上述定理出发，利用K_0-群项刻画了某些解析Toeplitz算子的相似不变量.
The famous von Neumann-Wold Theorem tells us that each analytic Toeplitz operator withn+ 1-Blaschke factors is unitary ton+ 1 copies of the unilateral shift on the Hardy space. It is obvious that the von Neumann-Wold Theorem does not hold in the Bergman space. In this paper, using the basis constructed by Michael and Zhu on the Bergman space we prove that each analytic Toeplitz operatorMB(z)is similar ton+ 1 copies of the Bergman shift if and only ifB(z) is ann+ 1-Blaschke product. From the above theorem, we characterize the similarity invariant of some analytic Toeplitz operators by usingK0-group term.