| Bergman空间上的斜Toeplitz算子 |
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| 引用本文： | 安恒斌,蹇人宜.Bergman空间上的斜Toeplitz算子[J].数学学报,2004,47(1):103-110. |
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| 作者姓名： | 安恒斌 蹇人宜 |
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| 作者单位： | 1. 中国科学院数学与系统科学研究院计算数学与科学工程计算研究所,北京,100080
2. 西北第二民族学院信息与计算科学系,银川,750021 |
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| 基金项目： | 宁夏回族自治区自然科学基金资助项目(99A003) |
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| 摘 要： | 本文讨论了Bergman空间上斜Toeplitz算子的若干性质,证明了:如果线性算子S在每个Lap(1
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| 关 键 词： | Berezin变换 Bergman空间 Toeplitz算子 |
| 文章编号： | 0583-1431(2004)01-0103-08 |
Slant Toeplitz Operators on Bergman Space |
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| Heng Bin AN.Slant Toeplitz Operators on Bergman Space[J].Acta Mathematica Sinica,2004,47(1):103-110. |
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| Authors: | Heng Bin AN |
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| Affiliation: | Heng Bin AN
(Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P. R. China)
Ren Yi JIAN
(Deparatment of Information and Computing Science, The Second Northwest Institute for Ethnic Minorities, Yinchuan 750021, P. R. China) |
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| Abstract: | In this paper, we set up some operator properties of slant Toeplitz operators on Bergman space. We prove that if S is a linear operator on every Lap (1 < p < ∞), then 5 is compact on La2 if and only if S(z), the Berezin transform of S, satisfies S(z)→0 (z→(?)D). Our main result can be used to prove that if S is a finite sum of finite products of Toeplitz operators or slant Toeplitz operators, then S is compact if and only if S(z)→0 as z→(?)D. |
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| Keywords: | Berezin transform Bergman space Toeplitz operator |
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