| Dirichlet型空间上Toeplitz算子的本性范数 |
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| 引用本文： | 陈建军,肖杰胜.Dirichlet型空间上Toeplitz算子的本性范数[J].数学研究及应用,2021,41(4):393-400. |
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| 作者姓名： | 陈建军 肖杰胜 |
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| 作者单位： | 肇庆学院数学与统计学院, 广东 肇庆 526061; 中山大学数学学院, 广东 广州 510275;嘉兴学院南湖学院, 浙江 嘉兴 314001; 中山大学数学学院, 广东 广州 510275 |
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| 基金项目： | 国家自然科学基金青年科学基金项目(Grant No.12001482), 肇庆市科技创新指导类项目(Grant No.202004031503), 肇庆学院自然科学项目青年项目(Grant No.221622), 肇庆学院创新科研团队资助项目, 肇庆学院优秀青年教师科研能力提升计划资助项目(Grant No.ZQ202108). |
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| 摘 要： | 本文研究单位圆盘上Dirichlet型空间非紧Toeplitz算子的本性范数, 它事实上等于到紧Toeplitz算子集的距离. 并且这个距离可由无限多个紧Toeplitz算子来刻画, 这个结果与加权Bergman空间情形的类似.
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| 关 键 词： | 本性范数 Toeplitz算子 Dirichlet型空间 |
| 收稿时间： | 2020/9/26 0:00:00 |
| 修稿时间： | 2021/1/15 0:00:00 |
Essential Norm of Toeplitz Operators on Dirichlet-Type Spaces |
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| Jianjun CHEN,Jiesheng XIAO.Essential Norm of Toeplitz Operators on Dirichlet-Type Spaces[J].Journal of Mathematical Research with Applications,2021,41(4):393-400. |
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| Authors: | Jianjun CHEN Jiesheng XIAO |
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| Institution: | School of Mathematics and Statistics, Zhaoqing University, Guangdong 526061, P. R. China; School of Mathematics, Sun Yat-sen University, Guangdong 510275, P. R. China; Nanhu College, Jiaxing University, Zhejiang 314001, P. R. China; School of Mathematics, Sun Yat-sen University, Guangdong 510275, P. R. China |
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| Abstract: | In this paper, we show that, on the Dirichlet-type space of unit disk, the essential norm of a noncompact Toeplitz operator equals its distance to the set of compact Toeplitz operators, and moreover, this distance is realized by infinitely many compact Toeplitz operators, which is analogous to the case of the weighted Bergman space. |
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| Keywords: | Essential norm Toeplitz operator Dirichlet-type space |
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