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Banach空间中线性算子广义逆的连续性及其应用

 引用本文: 黄强联, 马吉溥. Banach空间中线性算子广义逆的连续性及其应用[J]. 应用数学和力学, 2005, 26(12): 1500-1506.
HUANG Qiang-lian, MA Ji-pu. Continuity of Generalized Inverses of Linear Operators in Banach Spaces and Its Applications[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1500-1506.
 Citation: HUANG Qiang-lian, MA Ji-pu. Continuity of Generalized Inverses of Linear Operators in Banach Spaces and Its Applications[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1500-1506.

## Banach空间中线性算子广义逆的连续性及其应用

###### 作者简介:黄强联(1975- ),男,江苏盐城人,讲师,博士(联系人.Tel:+86-514-7862440;Fax:+86-514-7975462;E-mail:qlhmath@yahoo.com.cn)
• 中图分类号: O177.2

## Continuity of Generalized Inverses of Linear Operators in Banach Spaces and Its Applications

• 摘要: 研究了Banach空间中广义逆的扰动问题．给出了广义逆稳定的一些新特征,进而证明了这些稳定性特征与广义逆的选取无关,并由此得到了广义逆作为集值映射是下半连续的充要条件．
•  [1] Nashed M Z,Vortruba G F.A unified operator theory of generalized inverses[A].In: Nashed M Z Ed.Generalized Inverses and Applications[C].New York:Academic Press,1976,1—110. [2] Nashed M Z,Chen X.Convergence of Newton-like methods for singular equations using outer inverses[J].Numer Math,1993,66(2):235—257. [3] CHEN Guo-liang,XUE Yi-feng.Perturbation analysis for the operator equation Tx=b in Banach spaces[J].J Math Anal Appl,1997,212(1):107—125. [4] MA Ji-pu.(1.2) inverses of operators between Banach spaces and local conjugacy theorem[J].Chinese Ann Math Ser B,1999,20(1):57—62. [5] CHEN Guo-liang,XUE Yi-feng.The expression of the generalized inverse of the perturbed operator under type I perturbation in Hilbert spaces[J].Linear Algebra Appl,1998,285(1):1—6. [6] Ben-Israel A,Greville T N E.Generalized Inverses: Theory and Applications[M].New York:John Wiley and Sons,1974. [7] Ding J,Huang L J.On the continuity of generalized inverses of linear operators in Hilbert spaces[J].Linear Algebra Appl, 1997,262(2):229—242. [8] MA Ji-pu.Continuously sufficient and necessary conditions for Moore-Penrose inverses A+x[J].Scince in China Ser A,1990,33(11):1294—1302. [9] MA Ji-pu.On the necessary and sufficient conditions of the continuity of M-P inverses A+x[J].Chinese Ann Math，Ser B,1992,13(2):251—256. [10] Nashed M Z.Perturbations and approximations for generalized inverses and linear operators equations[A].In:Nashed M Z Ed.Generalized Inverses and Applications[C].New York:Academic Press,1976,325—396. [11] Aubin J P,Cellina A.Differential Inclusions[M].Berlin:Springer-Verlag,1984. [12] Kato T.Perturbation Theory for Linear Operators[M].New York:Springer-Verlag,1984.
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##### 出版历程
• 收稿日期:  2003-12-09
• 修回日期:  2005-06-16
• 刊出日期:  2005-12-15

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