| Hilbert空间上两个幂等算子组合的Drazin逆 |
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| 引用本文： | 周建新,汪金汉,陈敬华.Hilbert空间上两个幂等算子组合的Drazin逆[J].湖北师范学院学报(自然科学版),2014(2):23-27. |
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| 作者姓名： | 周建新 汪金汉 陈敬华 |
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| 作者单位： | 湖北师范学院数学与统计学院,湖北黄石435002 |
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| 基金项目： | 湖北省教育厅重点项目（D20122202）; 湖北省教育厅青年项目（B20122203） |
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| 摘 要： | 讨论了Hilbert空间上的两个不同的幂等算子P、Q的组合aP+bQ-cPQ的Drazin可逆性问题,利用幂等算子的性质和空间分解的技巧证明了aP+bQ-cPQ的Drazin逆在条件PQP=0下是存在的,并且给出了其逆的计算公式,其中a,b,c∈C,ab≠0.
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| 关 键 词： | 幂等算子 Drazin逆 幂等算子的组合 |
The Drazin invertibility of combinations of two idempotent operators over a Hilbert space |
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| ZHOU Jian-xin,WANG Jin-han,CHEN Jing-hua.The Drazin invertibility of combinations of two idempotent operators over a Hilbert space[J].Journal of Hubei Normal University(Natural Science),2014(2):23-27. |
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| Authors: | ZHOU Jian-xin WANG Jin-han CHEN Jing-hua |
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| Institution: | (College of Mathematical and Stastical, Hubei Normal University, Huangshi 435002, China) |
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| Abstract: | Discussed the problem of Drazin invertibility of combinations of two idempotent operators P、Q on a Hilbert space.By using the properties of idempotent operators and the techniques of space decomposition,prove the existance of Drazin invertibility of the combinations aP ＋ bQ-cPQ and its expression is also obtained,where a,b,c∈C,ab≠0. |
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| Keywords: | Idempotent operator Drazin invertibility combinations of idempotent operators |
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