| 林鸿钊,胡寅寅,卢玉峰.双圆盘加权Dirichlet空间上Toeplitz算子的约化子空间[J].数学年刊A辑,2016,37(3):311~328 |
| 双圆盘加权Dirichlet空间上Toeplitz算子的约化子空间 |
| Reducing Subspaces of Toeplitz Operator on the Weighted Dirichlet Space of the Bidisk |
| Received:June 26, 2014 Revised:September 27, 2015 |
| DOI： |
| 中文关键词: 约化子空间, Toeplitz 算子, Dirichlet 空间, 双圆盘 |
| 英文关键词:Reducing subspaces, Toeplitz operators, Dirichlet space, Bidisk |
| 基金项目:本文受到国家自然科学基金 (No.11271059) 的资助. |
| Author Name | Affiliation | | School of Mathematical Sciences, Dalian University of Technology,
Dalian 116024, Liaoning, China; College of Computer and Information Sciences, Fujian Agriculture and
Forestry University, Fuzhou 350002, China. | 大连理工大学数学科学学院, 辽宁\大连 116024
福建农林大学计算机与信息学院, 福州 350002. | | School of Mathematical Sciences, Dalian University of Technology,
Dalian 116024, Liaoning, China. | 大连理工大学数学科学学院, 辽宁\大连 116024. | | Corresponding author. School of Mathematical Sciences, Dalian University of Technology,
Dalian 116024, Liaoning, China. | 通讯作者. 大连理工大学数学科学学院, 辽宁\大连 116024 |
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| 中文摘要: |
| 刻画了双圆盘加权~Dirichlet~空间${\mathcal{D}}_\alpha({{{\mathbb{D}}}^{2}})$上~Toeplitz~算
子$T_{z_1^N}$ (或$T_{z_2^N}$)和$T_{z_1^Nz_2^N}$
的约化子空间. 结果表明~Toeplitz~算子$T_{z_1^N}$ (或$T_{z_2^N}$)的约化子空间结构与权系数$\alpha$无关,
而~Toeplitz~算子$T_{z_1^Nz_2^N}$的约化子空间结构与权系数$\alpha$有关. |
| 英文摘要: |
| In this paper, the authors describe the reducing subspaces of
Toeplitz operators $T_{z_1^N}$ (or $T_{z_2^N}$) and $T_{z_1^Nz_2^N}$
on the weighted Dirichlet space of the bidisk
${\mathcal{D}}_\alpha({{{\mathbb{D}}}^{2}})$. They show that
the structure of the reducing subspaces of $T_{z_1^N}$ (or
$T_{z_2^N}$) is independent of the weight $\alpha$, while for
$T_{z_1^Nz_2^N}$, the situation is different. |
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