| 关于算子方程AX=XAX与AX=XA=XAX |
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| 引用本文： | 安桂梅,白朝芳,杜拴平.关于算子方程AX=XAX与AX=XA=XAX[J].应用泛函分析学报,2003,5(1):9-12. |
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| 作者姓名： | 安桂梅 白朝芳 杜拴平 |
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| 作者单位： | 山西师范大学数学与计算机系,山西,临汾,041004 |
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| 基金项目： | NNSF of China，the NSF of Shanxi Province and the Youth Scientific and Technological
Foundation of Shanxi Province |
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| 摘 要： | 用A的不变子空间作参数，给出了算子方程AX＝XAX的全部解。当A是单射或稠值域时，或者当A是正规算子时，给出了算子方程AX＝XA＝XAX的全部解。我们还给出正规算子X是算子方程AX＝XZ＝XAX的解的充分必要条件。
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| 关 键 词： | 不变子空间 正规算子 Hilbert空间 级化子空间 算子方程 |
On the Operator Equations AX=XAX and AX=XA=XAX |
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| AN Gui-mei,BAI Zhao-fang,DU Shuan-ping.On the Operator Equations AX=XAX and AX=XA=XAX[J].Acta Analysis Functionalis Applicata,2003,5(1):9-12. |
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| Authors: | AN Gui-mei BAI Zhao-fang DU Shuan-ping |
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| Abstract: | in this paper, we give the representation of th E solution set of the operator equation ax=xax in terms of the invariant subs Paces of a and the representation of solution set of ax=xa=xax i N the cases that a is a normal operator or an operator with dense range or w Ith injectivity. We also give a sufficient and necessary condition for a normal Operator x to be a solution of equation xax=xa=xa.= |
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| Keywords: | operator equations invariant subspaces reducing subspaces normal operators |
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