| 多圆盘上的Toeplitz算子的紧的乘积 |
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| 引用本文： | 丁宣浩.多圆盘上的Toeplitz算子的紧的乘积[J].数学学报,2005,48(3):493-498. |
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| 作者姓名： | 丁宣浩 |
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| 作者单位： | 桂林电子工业学院计算科学与数学系 桂林541004 |
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| 基金项目： | 国家自然科学基金资助项目(10361003)
广西自然科学基金资助项目 |
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| 摘 要： | 对于多圆盘上的有界多重调和函数f,g,我们证明多圆盘Bergman空间上的Toeplitz算子的乘积TfTg是紧算子的充要条件是TfTg是零.这等价于f或g是零.换位子TfTg-TgTf是紧算子当且仅当换位子TfTg-TgTf是零.这等价于对每一个j,存在不全为零的常数αj和βj,使得αjf+βjg关于变量zj(1≤j≤n)是常数.
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| 关 键 词： | Toeplitz算子 紧算子 多圆盘 |
Compact Product of Toeplitz Operators on the Polydisk |
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| Xuan Hao DING.Compact Product of Toeplitz Operators on the Polydisk[J].Acta Mathematica Sinica,2005,48(3):493-498. |
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| Authors: | Xuan Hao DING |
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| Institution: | Xuan Hao DING Department of Computing Science and Mathematics, Guilin Institute of Electronic Technology, Guilin 541004, P. R. China |
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| Abstract: | For bounded pluriharmonic functions f, g on the polydisk, we show that two Toeplitz operators product TfTg on the Bergman space of the polydisk is compact if and only if TfTg = 0, or if and only if f or g is zero; TfTg - TgTf is compact if and only if TfTg - TgTf = 0, or if and only if for every j, there are constants αj and βj, not both zero, such that αjf + βjg is constant in variable zj (1≤j ≤ n). |
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| Keywords: | Toeplitz operators Compact operators Polydisk |
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