| Jong Soo AN.[J].数学年刊A辑,1999,20(3):317~324 |
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| A CRITERION OF ESSENTIALLY COMMUTING TOEPLITZ OPERATORSON BERGMAN SPACE |
| Received:April 10, 1998 Revised:July 06, 1998 |
| DOI： |
| 中文关键词: |
| 英文关键词:Bergman space, Toeplitz operator, Unit ball |
| 基金项目: |
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| 中文摘要: |
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| 英文摘要: |
| On the setting of the unit ball $U$ the author considers Toeplitz operators on
Bergman space. The Bergman space $B^p(U)\ (1\le p<\infty)$ is the closed subspace
of the usual Lebesgue space $L^p(U)$ consisting of holomorphic functions.
For a function $\beta\in L^2(U),$ the Toeplitz operator $T_{\beta}$ with symbol
$\beta$ is defined by $T_{\beta}f=\wp(\beta f)$ for function $f\in B^2(U)$.
Here $\wp$ is the Bergman projection from $L^2(U)$ onto $B^2(U)$. Two
bounded linear operators $S, T$ on the Hilbert $H$ are said to be essentially
commuting on $H$ if the commutator $ST-TS$ is compact on $H$. In this paper,
a criterion of essentially Toeplitz operators with the vanishing property
is obtained. |
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