| 包含广义逆的算子乘积的谱 |
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| 引用本文： | 杜鸿科,陆建明,高桂宝. 包含广义逆的算子乘积的谱[J]. 系统科学与数学, 2009, 29(2): 184-190 |
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| 作者姓名： | 杜鸿科 陆建明 高桂宝 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,西安,710062 |
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| 摘 要： | 给定三个算子A,B,C∈ B(H),其中算子B的值域R(B)是闭的,利用算子矩阵分块技巧给出了∪σ(AB(1))C)=C的充分必要条件,其中σ(D)是算子D ∈B(H)的B(1) ∈B{1}谱,B{1}={X∈B(H):B×B=B}.
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| 关 键 词： | 谱 广义逆 Moore-Penrose逆 |
| 收稿时间： | 2006-12-13 |
| 修稿时间： | 2007-12-10 |
Spectra of Operator Products Involving GeneralizedInverses |
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| DU Hong-ke,LU Jian-ming,GAO Gui-bao. Spectra of Operator Products Involving GeneralizedInverses[J]. Journal of Systems Science and Mathematical Sciences, 2009, 29(2): 184-190 |
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| Authors: | DU Hong-ke LU Jian-ming GAO Gui-bao |
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| Affiliation: | College of Mathematics and Information Science,Shaanxi Normal University, Xi'an 710062 |
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| Abstract: | Let $mathcal {B(H)}$ denote the set of all bounded linear operatorson a Hilbert space $mathcal H$. In this note, for three operators$A$, $B$ and $Cin mathcal {B(H)}$, if the range ${mathcal R}(B)$of $B$ is closed, then the necessary and sufficient conditions suchthat $bigcuplimits_{B^{(1)}in B{1}}sigma(AB^{(1)}C)=C$ is obtained by using block-operator matrix technique, where$sigma(D)$ is the spectrum of an operator $Din {mathcal {B(H)}}$and$B{1}:={Xin {mathcal {B(H)}}:BXB=B}.$ |
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| Keywords: | Spectra generalized inverse Moore-Penrose inverse. |
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