| 不同Bers型空间之间的加权复合算子 |
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| 引用本文： | 王茂发,刘云.不同Bers型空间之间的加权复合算子[J].数学物理学报(A辑),2007,27(4):665-671. |
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| 作者姓名： | 王茂发 刘云 |
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| 作者单位： | 武汉大学数学与统计学院，荆楚理工学院数学系 武汉 430072，沙洋 448200 |
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| 摘 要： | 该文讨论了单位圆盘上不同Bers型空间之间的加权复合算子的有界性、紧性和弱紧性, 给出了一些充分必要的判别条件, 特别地得到不同Bers型空间上加权复合算子的紧性与弱紧性的等价性. 这些推广了经典的复合算子与乘法算子的相关结论. 该文同时也给出了Bers型空间上复合算子的Fredholm性和闭值域问题的刻画, 完善了文献6]中结论.
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| 关 键 词： | 加权复合算子 Fredholm 算子 Bers型空间 闭值域 有界性 弱紧性 |
| 文章编号： | 1003-3998（2007）04-665-07 |
| 收稿时间： | 2005-12-19 |
| 修稿时间： | 2005-12-19 |
Weighted Composition Operators between Bers-type Spaces |
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Wang Maofa,Liu Yun
.Weighted Composition Operators between Bers-type Spaces[J].Acta Mathematica Scientia,2007,27(4):665-671. |
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| Authors: | Wang Maofa Liu Yun
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| Institution: | 1.School of Mathematics and Statistics, Wuhan University, Wuhan 430072;2.Department of Mathematics, Jingchu University of Technology, Shayang 448200 |
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| Abstract: | In this paper,the authors study weighted composition operators between Bers-type spaces.Some sufficient and necessary conditions for such operators to be bounded,compact and weakly compact are given,respectively.This may be regarded as a generalization of the corresponding multiplication operator and composition operator cases.As a corollary, the authors obtain that the weak compactness and the compactness of weighted composition operators between Bers-type spaces are equivalent.In addition,the authors also characterize composition operators which have Fredholm properties and closed range on Bers-type spaces, respectively. |
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| Keywords: | Weighted composition operator Fredholm operator Bers-type space Closed range Boundedness Weak compactness |
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