Centralizers of Toeplitz Operators with Polynomial Symbols
Centralizers of Toeplitz Operators with Polynomial Symbols
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DOI：
10.1007/s11785-011-0150-5
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发表时间：
2010-08
影响因子：
0.8
通讯作者：
A. Tikaradze
中科院分区：
文献类型：
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作者：
A. Tikaradze
在这篇注记中，我们描述了Bergman空间上具有多项式符号的Toeplitz算子的中心化。结果表明，如果由所有Toeplitz算子生成的范数闭代数的一个元素与非常数多项式的Toeplitz算子交换，则该元素是全纯函数的Toeplitz算子。
In this note we describe centralizers of Toeplitz operators with polynomial symbols on the Bergman space. As a consequence it is shown that if an element of the norm closed algebra generated by all Toeplitz operators commutes with a Toeplitz operator of a nonconstant polynomial, then this element is a Toeplitz operator of a holomorphic function.