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].
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页码：129 / 168
页数：40
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