Volterra算子与Toeplitz算子的乘积

数学物理学报 ›› 2024, Vol. 44 ›› Issue (4): 829-836.

Volterra算子与Toeplitz算子的乘积

丁宣浩^1,²(),邵长慧¹(),李永宁^1,^2,^*()

¹重庆工商大学数学与统计学院重庆 400067
²经济社会应用统计重庆市重点实验室重庆 400067

收稿日期:2023-05-25 修回日期:2023-10-12 出版日期:2024-08-26 发布日期:2024-07-26
通讯作者: *李永宁, E-mail:yongningli@ctbu.edu.cn
作者简介:丁宣浩, E-mail:dingxuanhao@ctbu.edu.cn;|邵长慧, E-mail: schdliyx@163.com
基金资助:
国家自然科学基金(12101092);重庆市自然科学基金(CSTB2022NSCQ-MSX1045);重庆市教委科学技术研究项目(KJQN202100822)

The Product of Volterra Operator and Toeplitz Operator

Ding Xuanhao^1,²(),Shao Changhui¹(),Li Yongning^1,^2,^*()

¹School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067
²Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing 400067

Received:2023-05-25 Revised:2023-10-12 Online:2024-08-26 Published:2024-07-26
Supported by:
National Natural Science Foundation of China(12101092);Chongqing Natural Science Foundation(CSTB2022NSCQ-MSX1045);Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN202100822)

摘要/Abstract

摘要：

该文研究了经典 Hardy 空间上的 Volterra 算子 $ V $ 与 Toeplitz 算子 $ T_\varphi $ 的乘积算子 $ L_\varphi= T_\varphi V $ 与 $ R_\varphi= VT_\varphi $, 得到了 $ L_\varphi $ 与 $ R_\varphi $ 的一些基本性质, 并给出了 $ L_\varphi $ 的类似于 Toeplitz 算子的 Coburn 定理的结果. 该文还给出了 $ V $ 和 $ T_\varphi $ 可交换的充分必要条件, 以及 $ L_\varphi $ 及 $ R_\varphi $ 以 $ z^jH^2 $ $ (j=1, 2, \cdots ) $ 为不变子空间的符号的充要刻画.

关键词: Volterra 算子, Toeplitz 算子, Coburn 定理, 可交换, 不变子空间

Abstract:

In this paper, we study the product operators of Volterra operator $ V $ and Toeplitz operator $ T_\varphi $ on the classical Hardy space $ L_\varphi=T_\varphi V $ and $ R_\varphi=VT_\varphi $, and we obtain some basic properties of $ L_\varphi $ and $ R_\varphi $, we also get a result of $ L_\varphi $ which is similar to the Coburn theorem of Toeplitz operator. The necessary and sufficient conditions for $ V $ and $ T_\varphi $ to be commutative are given in this paper, and the symbol of $ L_\varphi $ and $ R_\varphi $ is characterized when $ z^jH^2\ (j=1, 2, \cdots ) $ are the common invariant subspaces of $ L_\varphi $ and $ R_\varphi $.

Key words: Volterra operator, Toeplitz operator, Coburn theorem, Commutative, Invariant subspace

中图分类号:

O177.1

丁宣浩, 邵长慧, 李永宁. Volterra算子与Toeplitz算子的乘积[J]. 数学物理学报, 2024, 44(4): 829-836.

Ding Xuanhao, Shao Changhui, Li Yongning. The Product of Volterra Operator and Toeplitz Operator[J]. Acta mathematica scientia,Series A, 2024, 44(4): 829-836.

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