| Dirichlet空间上一类Toeplitz算子 |
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| 引用本文： | 王晓峰,夏锦.Dirichlet空间上一类Toeplitz算子[J].四川师范大学学报(自然科学版),2006,29(5):577-579. |
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| 作者姓名： | 王晓峰 夏锦 |
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| 作者单位： | 广州大学,数学与信息科学学院,广东,广州,510006 |
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| 摘 要： | 讨论了单位圆盘上Sobolev空间中解析函数组成子空间，Dirichlet空间上符号为径向函数（即函数只与自变量的模相关的函数）的Toeplitz算子．得到Toeplitz算子的有界性与一个符号函数相关数列有界性等价，紧性与这个数列收敛到零等价，并用这个数列表出了Toeplitz算子的点谱和谱．
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| 关 键 词： | Dirichlet空间 Toeplitz算子 谱 紧算子 |
| 文章编号： | 1001-8395（2006）05-0577-03 |
| 收稿时间： | 2005-12-12 |
| 修稿时间： | 2005年12月12 |
A Class of Toeplitz Operators on Dirichlet Spaces |
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| WANG Xiao-feng,XIA Jin.A Class of Toeplitz Operators on Dirichlet Spaces[J].Journal of Sichuan Normal University(Natural Science),2006,29(5):577-579. |
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| Authors: | WANG Xiao-feng XIA Jin |
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| Affiliation: | Deparment of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, Guangdong |
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| Abstract: | A Dirichlet space is a subspace consisting of analytic functions of a Sobolev space on the unit disc.In this paper,Toeplitz operators on a Dirichlet space with radical symbol functions(i.e.,functions related only to the norm of variables) are discussed.It is proved that the boundedness of a Toeplitz operator is equivalent to the boundedness of a number series corresponding to the symbol function.It is also proved that the compactness of the operator is equivalent to that the series is convergent to 0.Finally,the point spectra and spectra of Toeplitz operators are represented by these serieses. |
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| Keywords: | Dirichlet spaces Toeplitz operators Spectra Compact operator |
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