| Cowen-Douglas算子的交换子 |
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| 引用本文： | 靳勇飞,王宗尧.Cowen-Douglas算子的交换子[J].数学学报,2006,49(1):69-76. |
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| 作者姓名： | 靳勇飞 王宗尧 |
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| 作者单位： | 华东理工大学数学系,上海200237 |
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| 基金项目： | 国家自然科学丛金资助项目（10071020） |
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| 摘 要： | 设H是一个可分的Hilbert空间,(?)(H)是H上的有界线性算子全体．对 A∈(?)(H),(?)’(A)={B∈(?)(H):AB=BA},rad(?)’(A)表示(?)’(A)的Jacob son根．本文首先举例说明了存在Cowen-Douglas算子T,商代数(?)’(T)／rad(?)’(T) 可以是不交换的．在给出了使得(?)’(T)／rad(?)’(T)交换的充分条件之后,证明了使得 (?)’(T)／rad(?)’(T)交换的Cowen-Douglas算子在Bn(Ω)中是稠密的．对Bmn(Ω),得到了类似的结果。
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| 关 键 词： | Cowen-Douglas算子 交换子 Jacobson根 |
| 文章编号： | 0583-1431（2006）01-0069-08 |
| 收稿时间： | 2004-08-15 |
| 修稿时间： | 2004-08-152004-10-25 |
About the Commutant of Cowen-Douglas Operators |
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| Yong Fei JIN, Zong Yao WANG.About the Commutant of Cowen-Douglas Operators[J].Acta Mathematica Sinica,2006,49(1):69-76. |
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| Authors: | Yong Fei JIN Zong Yao WANG |
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| Institution: | Yong Fei JIN Zong Yao WANG Department of Mathematics, East China University of Science and Technology, Shanghai 200237, P. R. China |
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| Abstract: | Let H be a complex seperable Hilbert space and L(H) denote the collection of bounded linear operators on H. In this paper, we first show that the quotient algebra (?)'(T)/rad(?)'(T) is not always commutative for each T ∈ Bn(Ω). Then after giving a sufficient condition for (?)'(T)/rad.(?)'(T) to be commutative, we show that the set of ,Bbn(Ω) operators A, with (?)'(A)/rad(?)'(A) commutative, is dense in Bn(Ω). Similar results are also established for Bmn(Ω) operators. |
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| Keywords: | Cowen-Douglas operator commutant jacobson radical |
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