Multiplication operators on the Bergman space via the Hardy space of the bidisk

被引：49

作者：

Guo, Kunyu ^{[1
]}

Sun, Shunhua ^{[2
]}

Zheng, Dechao ^{[3
]}

Zhong, Changyong ^{[4
]}

机构：

[1] Fudan Univ, Dept Math, Shanghai 200433, Peoples R China

[2] Jiaxing Univ, Inst Math, Jiaxing 314001, Zhejiang, Peoples R China

[3] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

[4] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2009年 / 628卷

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

ANALYTIC TOEPLITZ-OPERATORS; REDUCING SUBSPACES; COMMUTANT; THEOREM; FORMS;

D O I：

10.1515/CRELLE.2009.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we develop a machinery to study multiplication operators on the Bergman space via the Hardy space of the bidisk. Using the machinery we study the structure of reducing subspaces of a multiplication operator on the Bergman space. As a consequence, we completely classify reducing subspaces of the multiplication operator by a Blaschke product phi with order three on the Bergman space to solve a conjecture of Zhu [40].

引用

页码：129 / 168

页数：40

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