| Dirichlet空间上的超循环复合算子 |
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| 引用本文： | 曹志平,曹广福. Dirichlet空间上的超循环复合算子[J]. 数学年刊A辑(中文版), 2005, 0(3) |
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| 作者姓名： | 曹志平 曹广福 |
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| 作者单位： | 四川大学数学学院，广州大学数学与信息科学院 成都 610064，广州 510405 |
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| 基金项目： | 国家自然科学基金(No．10371082)资助的项目． |
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| 摘 要： | 设Bn是复平面C中的单位圆盘(n=1)或复空间Cn中的单位球.众所周知,在Hardy空间上存在丰富的符号在Aut(Bn)中的超循环复合算子.然而,在复平面中单位圆盘上的Dirichlet空间中, 任何复合算子都不能是超循环的.本文则证明,当n>1时,Bn上的Dirichlet空间中确有超循环复合算子.
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| 关 键 词： | Dirichlet空间 循环算子 超循环算子 复合算子 |
HYPERCYCLIC COMPOSITION OPERATORS ON DIRICHLET SPACES |
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| CAO Zhiping CAO Guangfu College of Mathematics,Sichuan University,Chengdu ,China. College of Mathematics and Information Science,Guangzhou University,Guangzhou ,China.. HYPERCYCLIC COMPOSITION OPERATORS ON DIRICHLET SPACES[J]. Chinese Annals of Mathematics, 2005, 0(3) |
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| Authors: | CAO Zhiping CAO Guangfu College of Mathematics Sichuan University Chengdu China. College of Mathematics Information Science Guangzhou University Guangzhou China. |
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| Affiliation: | CAO Zhiping CAO Guangfu College of Mathematics,Sichuan University,Chengdu 610064,China. College of Mathematics and Information Science,Guangzhou University,Guangzhou 510405,China. |
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| Abstract: | It is well-known that there are hypercyclic composition operators with symbols in Aut(Bn) on hardy space, where Bn is the unit disk in complex plane C or the unit ball in n-dimensional complex space Cn. However, any composition operator on Dirichlet space D for one complex variable can not be hypercyclic. In the present paper, the authors prove that there are indeed hypercyclic composition operators on Dirichlet spaces for several complex variables. |
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| Keywords: | Dirichlet space. Cyclic operators Hypercyclic operator Composition operstor |
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