Classification of Reducing Subspaces of a Class of Multiplication Operators on the Bergman Space via the Hardy Space of the Bidisk

被引：31

作者：

Sun, Shunhua ^{[1
]}

Zheng, Dechao ^{[2
]}

Zhong, Changyong ^{[3
]}

机构：

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

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

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

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2010年 / 62卷 / 02期

基金：

中国国家自然科学基金;

关键词：

TOEPLITZ-OPERATORS; FORMS;

D O I：

10.4153/CJM-2010-026-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we obtain a complete description of nontrivial minimal reducing subspaces of the multiplication operator by a Blaschke product with four zeros on the Bergman space of the unit disk via the Hardy space of the bidisk.

引用

页码：415 / 438

页数：24

共 21 条

[1] [Anonymous], 1989, PITMAN RES NOTES MAT
[2] THEOREM ON ENTIRE FUNCTIONS WITH APPLICATIONS TO TOEPLITZ OPERATORS
BAKER, IN
DEDDENS, JA
ULLMAN, JL
[J]. DUKE MATHEMATICAL JOURNAL, 1974, 41 (04) : 739 - 745
[3] HARDY SPACE EXPECTATION OPERATORS AND REDUCING SUBSPACES
BALL, JA
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 47 (02) : 351 - 357
[4] BERCOVICI H, 1985, CBMS REGIONAL C SERI, V56
[5] ON A CLASS OF OPERATORS
BROWN, A
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1953, 4 (05) : 723 - 728
[6] Operator theory in the Hardy space over the bidisk
Douglas, RG
Yang, RW
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2000, 38 (02) : 207 - 221
[7] Ferguson SH, 2005, MATH SCAND, V96, P117
[8] FERGUSON SH, 2006, THETA SER ADV MATH, V6, P93
[9] Multiplication operators on the Bergman space via the Hardy space of the bidisk
Guo, Kunyu
Sun, Shunhua
Zheng, Dechao
Zhong, Changyong
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2009, 628 : 129 - 168
[10] Halmos P. R., 1961, J. Reine Angew. Math, V208, P102

← 1 2 3 →