| 丁宣浩.截断调和Bergman空间上的Toeplitz算子[J].数学年刊A辑,2013,34(1):81~86 |
| 截断调和Bergman空间上的Toeplitz算子 |
| Toeplitz Operators on the Cutoff Harmonic Bergman Space |
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| DOI： |
| 中文关键词: |
| 英文关键词:Cutoff harmonic Bergman space,Toeplitz |
| 基金项目:国家自然科学基金 (No.10871217) |
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| 中文摘要: |
| 截断调和Bergman空间$b^{2}_{n}=L^{2}_{a}\oplus\{\ov{w},\ov{w}^{2},\cdot\cdot\cdot,\ov{w}^{n}\}^{\vee}$是Hilbert空间$L^{2}$的闭子空间. 研究了单位圆盘上的截断调和Bergman空间上的Toeplitz算子的乘积问题, 完整地刻画了具有有界调和符号的两个Toeplitz算子的有限秩与紧的半换位子或换位子. |
| 英文摘要: |
| The cutoff harmonic Bergman space $b^{2}_{n},$ defined by $b^{2}_{n}=L^{2}_{a}\oplus \{\ov{w},\ov{w}^{2},\cdots,\ov{w}^{n}\}^{\vee},$ is a closed subspace of the Hilbert space$L^{2}$. The author studies the product problem of Toeplitz operators on the cutoff harmonic Bergman space on the unit disk, and completely characterizes the finite rank and the compact semi-commutator or the commutator of two Toeplitz operators with bounded harmonic symbols. |
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