| About Operator Weighted Shift |
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| 作者姓名： | Chun Lan JIANG Yong Fei JIN Zong Yao WANG |
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| 作者单位： | [1]Department of Mathematics, Hebei Normal University, Shifiazhuang 050016, P. R. China [2]Department of Mathematics, East China University of Science and Technology, Shanghai 200237, P. R. China |
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| 基金项目： | Work partialiy supported by NNSFC |
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| 摘 要： | Abstract Let H be a complex seperable Hilbert space and ~（Jt~） denote the collection of bounded linear operators on H. For an operator in L（H）, rad{A}＇ denotes the Jacobson radical of the commutant of A. This paper characterizes the similarity of strongly irreducible operator weighted shift in terms of {A}＇/rad{A}＇. Moreover, we suggest some ways to determine when an operator weighted shift is strongly irreducible and when its commutant is commutative.
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| 关 键 词： | 强不可约算子 加权算子 相似性 交换子 Hilbert空间 |
| 收稿时间： | 20 August 2004 |
| 修稿时间： | 2004-08-20 |
About Operator Weighted Shift |
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| Chun Lan JIANG Yong Fei JIN Zong Yao WANG.About Operator Weighted Shift[J].Acta Mathematica Sinica,2007,23(8):1385-1390. |
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| Authors: | Chun Lan Jiang Yong Fei Jin Zong Yao Wang |
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| Institution: | (1) Department of Mathematics, Hebei Normal University, Shijiazhuang, 050016, P. R. China;(2) 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 . For an operator
in ℒ(ℋ ), rad{A}' denotes the Jacobson radical of the commutant of A. This paper characterizes the similarity of strongly irreducible operator weighted shift in terms of {A}'/ rad{A}'. Moreover, we suggest some ways to determine when an operator weighted shift is strongly irreducible and when its commutant
is commutative.
Work partially supported by NNSFC |
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| Keywords: | Operator weighted shift Strongly irriducible operator Similarity Commutant Jacobson radical |
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