Unified Approach to the Expression for the Moore-Penrose Inverse of a- xy 被引量：1

Unified Approach to the Expression for the Moore-Penrose Inverse of a- xy

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摘要 Let A be an unital C*-algebra, a, x and y are elements in A. In this paper, we present a method how to calculate the Moore-Penrose inverse of a- xy*and investigate the expression for some new special cases of(a- xy*). Let .4 be an unital C＊-algebra, a,x and y are elements in .A. In this paper, we present a method how to calculate the Moore-Penrose inverse of a - xy＊ and investigate the expression for some new special cases of （a - xy）.

作者 D U Fa-peng XUE Yi-feng

机构地区 Department of Mathematics Department of Mathematics

出处《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第3期465-474,共10页 数学季刊（英文版）

基金 Supported by the NNSF of China(10771069)

关键词 C*-algebra generalized inverse Moore-Penrose inverse C＊-algebra generalized inverse Moore-Penrose inverse

分类号 O151.21 [理学—基础数学]

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参考文献15

1CHEN Guo-liang, XUE Yi-feng. The expression of generalized inverse of the perturbed operators under type 1 perturbation in Hilbert spacesf.I]. Linear Algebra Appl, 1998, 285: 1-6.
2CHEN Yong-hao, HU Xiao-xia, XU Qing-xiang. The Moore-Penrose inverse of A - XY*[J]. J Shanghai Normal Univer, 2009, 38: 15-19.
3DENG Chun-yuan. On the invertibility of the operator A - XB[J] , Numb Linear Algebra Appl, 2009, 16: 817-831.
4DENG Chun-yuan. A generalization of the Sherman-Morrison-Woodbury formula[J]. Appl Math Lett, 2011, 24: 1561- I564.
5DENG Chun-yuan. On Moore-Penrose inverse of a kind of operators[J]. Proceedings of the Ninth International Conference on Matrix Theory and Its Applications in China, 2010, 2: 88-91.
6DENG Chun-yuan, WEI Yi-min. Some new results of the Sherman-Morrison-Woodbury formula[J] , Proceeding of the Sixth International Conference of Matrices and Operators, 2011, 2: 220-223.
7DU Fa-peng,XUE Yi-feng.The Reverse Order Law for Moore-Penrose Inverse of Closed Operators[J].Chinese Quarterly Journal of Mathematics,2013,28(1):139-146. 被引量：3
8DU Fa-peng, XUE Yi-feng. The expression of the Moore-Penrose inverse of A — XV'fJ]. J East China Normal Univer(Nat Sci), 2010, 5: 33-37.
9HHATWIG R E. Block generalized inverses[J]. Arch Ratio Mech Anal, 1976, 61(3): 197-251.
10HSNDERSON H V, SEARL S R. On deriving the inverse of a sum of matrices[J] , Siam Review, 1981, 23(1): 53-60.

二级参考文献22

1BEN-ISRALE A, GREVILLE T N E. Generalized Inverse: Theory and Applications[M]. New York: Springer- Verlag, 2003.
2BOULDIN R H. The pseudo-inverse of a product[J]. SIAM J Appl Math, 1973, 25: 489-495.
3BOULDIN R H. Generalized inverses and factorizations, recent applications of generalized inverses[J]. Pit- man Ser Res Notes in Math, 1982~ 66: 233-248.
4CHEN Guo-liang, XUE Yi-feng. The expression of generalized inverse of the perturbed operators under type I perturbation in Hilbert spaces[J]. Linear Algebra Appl, 1998, 285: 1-6.
5CVETKOVIC-ILIC D C. Reverse order laws for (1, 3, 4)-generalized inverses in C-algebras[J]. Appl Math Lett, 2011, 24: 210-213.
6DJORDJEVIC D S. Further results on the reverse order law for generalized inverses[J]. SIAM J Matrix Anal Appl, 2007, 29 (4): 1242-1246.
7DJORDJEVIC D S, DINCIE, N,C. Reverse order law for Moore penrose inverses[J]. J Math Anal Appl, 2(110, 361: 252-261.
8DJORDJEVIC D S. Unified approach to the reverse order rule for generalized inverses[J]. Acta Sci Math(Szeg- ed), 2001, 167: 761-776.
9FURUTA T, NAKAMOTO R. Some theorems on certain contraction operators[J]. Proc Japan Acad, 1969, 45: 565-566.
10GALPERIN A M, WAKSMAN Z. On pseudoinverses of operator products[J]. Linear Algebra and Appl, 1980, 33: 123-131.

共引文献2

1杜法鹏.分块矩阵广义逆的表示[J].徐州工程学院学报（自然科学版）,2015,30(2):46-53.
2魏什笛,杜法鹏.A-XGY的Moore-Penrose逆的表示[J].高等学校计算数学学报,2015,37(3):228-233. 被引量：1

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1杜法鹏.Expression for the Group Inverse of the 2×2 Block Matrix[J].Chinese Quarterly Journal of Mathematics,2016,31(4):412-421.

1Hong-Kui Pang,Xiao-Qing Jin.Some Properties of the Optimal Preconditioner and the Generalized Superoptimal Preconditioner[J].Numerical Mathematics(Theory,Methods and Applications),2010,3(4):449-460.
2Cao WenshengInstitute of Math.,Xiangtan Polytechnic Univ.,Xiangtan 411201,China..SOLVABILITY OF A QUATERNION MATRIX EQUATION[J].Applied Mathematics(A Journal of Chinese Universities),2002,17(4):490-498. 被引量：2
3DU Fa-peng,XUE Yi-feng.The Reverse Order Law for Moore-Penrose Inverse of Closed Operators[J].Chinese Quarterly Journal of Mathematics,2013,28(1):139-146. 被引量：3
4Yongge TIAN,Wenxing GUO.Some Equalities and Inequalities for the Hermitian Moore-Penrose Inverse of Triple Matrix Product with Applications[J].Journal of Mathematical Research with Applications,2015,35(3):321-329.
5Tianxiao HE,Tung NGUYEN.A Unified Approach to Construct a Class of Daubechies Orthogonal Scaling Functions[J].Journal of Mathematical Research with Applications,2017,37(1):29-39.
6Chen Jianlong(Department of Mathematics and Mechanics, Southeast University, Naming, 210018).Moore-Penrose Inverses and Group Inverses of Block k-Circulant Matrices[J].Chinese Quarterly Journal of Mathematics,1996,11(1):86-99. 被引量：1
7LI YONG,WANG HUAIZHONG(Department of Matehematics,Jilin University, Changchun 130023, Jilin, China).COMPARISON　THEOREMS　TO　BOUNDARY　VALUE　PROBLEMS　FOR　ORDINARY　DIFFERENTIAL　EQUATIONS[J].Chinese Annals of Mathematics,Series B,1994,15(2):165-172.
8潘平奇,欧阳梓祥.MOORE-PENROSE INVERSE SIMPLEX ALGORITHMS BASED ON SUCCESSIVE LINEAR SUBPROGRAMMING APPROACH[J].Numerical Mathematics A Journal of Chinese Universities(English Series),1994,3(2):180-190.
9Tianxiao HE.A Unified Approach to Generalized Stirling Functions[J].Journal of Mathematical Research with Applications,2012,32(6):631-646.
10张化光,赵琰,余文,杨东升.A unified approach to fuzzy modelling and robust synchronization of different hyperchaotic systems[J].Chinese Physics B,2008,17(11):4056-4066. 被引量：4

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2014年第3期

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