Finite rank commutators and semicommutators of Toeplitz operators with harmonic symbols

被引：31

作者：

Guo, Kunyu ^{[1
]}

Sun, Shunhua ^{[2
]}

Zheng, Dechao ^{[3
]}

机构：

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

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

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

来源：

ILLINOIS JOURNAL OF MATHEMATICS | 2007年 / 51卷 / 02期

关键词：

D O I：

10.1215/ijm/1258138431

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we completely characterize finite rank semicommutator or commutator of two Toeplitz operators with bounded harmonic symbols on the Bergman space. We show that if the product of two Toeplitz operators with bounded harmonic symbols has finite rank, then one of the Toeplitz operators must be zero.

引用

页码：583 / 596

页数：14

共 17 条

[1] A theorem of Brown-Halmos type for Bergman space Toeplitz operators [J].

Ahern, P ;

Cuckovic, Z .

JOURNAL OF FUNCTIONAL ANALYSIS, 2001, 187 (01) :200-210

[2]

Axler S, 1998, INDIANA U MATH J, V47, P387

[3]

Axler S, 1998, STUD MATH, V127, P113

[4] COMMUTING TOEPLITZ-OPERATORS WITH HARMONIC SYMBOLS [J].

AXLER, S ;

CUCKOVIC, Z .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 1991, 14 (01) :1-12

[5]

AXLER S, 1988, LONGMAN SCI TECH, P1

[6]

AXLER S, 1978, INTEGR EQUAT OPER TH, V1, P285

[7]

AXLER S, 1988, SURVEYS SOME RECENT, V1

[8]

DING X, FINITE RANT COMMUTAT

[9]

ENGLIS M, 1996, ST PETERSBURG MATH J, V7, P89

[10]

GARNETT JB, 1981, PURE APPL MATH, V96

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