| Toeplitz算子在Dirichlet空间上的亚正规性 |
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| 引用本文： | 陆俏飞,于涛.Toeplitz算子在Dirichlet空间上的亚正规性[J].数学研究及应用,2011,31(6):1057-1063. |
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| 作者姓名： | 陆俏飞 于涛 |
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| 作者单位： | 浙江师范大学数理与信息工程学院，浙江 金华 321004;浙江师范大学数理与信息工程学院，浙江 金华 321004 |
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| 基金项目： | 国家自然科学基金(Grant No.10971195),浙江省自然科学基金(Grant Nos.Y6090689; Y6110260). |
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| 摘 要： | In this paper,we prove that the necessary and sufficient condition for a Toeplitz operator Tu on the Dirichlet space to be hyponormal is that the symbol u is constant for the case that the projection of u in the Dirichlet space is a polynomial and for the case that u is a class of special symbols,respectively.We also prove that a Toeplitz operator with harmonic polynomial symbol on the harmonic Dirichlet space is hyponormal if and only if its symbol is constant.
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| 关 键 词： | Dirichlet空间 Toeplitz算子 充分必要条件 空间投影 多项式 证明 谐波 |
| 收稿时间： | 6/1/2010 12:00:00 AM |
| 修稿时间： | 2011/1/12 0:00:00 |
Hyponormality of Toeplitz Operators on the Dirichlet Space |
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| Qiao Fei LU and Tao YU.Hyponormality of Toeplitz Operators on the Dirichlet Space[J].Journal of Mathematical Research with Applications,2011,31(6):1057-1063. |
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| Authors: | Qiao Fei LU and Tao YU |
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| Institution: | Department of Mathematics, Zhejiang Normal University, Zhejiang 321004, P. R. China |
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| Abstract: | In this paper, we prove that the necessary and sufficient condition for a Toeplitz operator $T_u$ on the Dirichlet space to be hyponormal is that the symbol $u$ is constant for the case that the projection of $u$ in the Dirichlet space is a polynomial and for the case that $u$ is a class of special symbols, respectively. We also prove that a Toeplitz operator with harmonic polynomial symbol on the harmonic Dirichlet space is hyponormal if and only if its symbol is constant. |
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| Keywords: | Toeplitz operator hyponormality Dirichlet space harmonic Dirichlet space |
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