Commutants of analytic Toeplitz operators on the harmonic Bergman space

被引：31
作者：
Choe, BR [1 ]
Lee, YJ [1 ]
机构：
[1] Korea Univ, Dept Math, Seoul 136713, South Korea
来源：
INTEGRAL EQUATIONS AND OPERATOR THEORY | 2004年 / 50卷 / 04期
关键词：
commutant; Toeplitz operator; harmonic Bergman space;
D O I：
10.1007/s00020-004-1338-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the commuting problem for Toeplitz operators on the harmonic Bergman space of the unit disk. We show that an analytic Toeplitz operator and a co-analytic Toeplitz operator with certain noncyclicity hypothesis can commute only when one of their symbols is constant. We also obtain analogous results for semi-commutants.
引用
收藏
页码：559 / 564
页数：6
相关论文
共 9 条
[1]   ALGEBRAS GENERATED BY ANALYTIC AND HARMONIC-FUNCTIONS [J].
AXLER, S ;
SHIELDS, A .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1987, 36 (03) :631-638
[2]   Commutants of analytic Toeplitz operators on the Bergman space [J].
Axler, S ;
Cuckovic, Z ;
Rao, NV .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (07) :1951-1953
[3]  
Choe BR, 1999, MICH MATH J, V46, P163
[4]   OPERATORS WITH DENSE, INVARIANT, CYCLIC VECTOR MANIFOLDS [J].
GODEFROY, G ;
SHAPIRO, JH .
JOURNAL OF FUNCTIONAL ANALYSIS, 1991, 98 (02) :229-269
[5]  
Hedenmalm H., 2000, Theory of Bergman spaces, DOI DOI 10.1007/978-1-4612-0497-8
[6]   Some differential and integral equations with applications to Toeplitz operators [J].
Lee, YJ ;
Zhu, KH .
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2002, 44 (04) :466-479
[7]  
Ross W. T., 2002, U LECT SERIES, V25
[8]  
Zhu K., 1990, Operator Theory in Function Spaces
[9]   Maximal inner spaces and Hankel operators on the Bergman space [J].
Zhu, KH .
INTEGRAL EQUATIONS AND OPERATOR THEORY, 1998, 31 (03) :371-387
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