Perturbations of Moore–Penrose Metric Generalized Inverses of Linear Operators in Banach Spaces  被引量:5

Perturbations of Moore–Penrose Metric Generalized Inverses of Linear Operators in Banach Spaces

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作  者:Hai Feng MA Shuang SUN Yu Wen WANG Wen Jing ZHENG 

机构地区:[1]School of Mathematical Science,Harbin Normal University [2]Department of Mathematics,Hulunbuir College

出  处:《Acta Mathematica Sinica,English Series》2014年第7期1109-1124,共16页数学学报(英文版)

基  金:supported by National Science Foundation of China,Tian Yuan Special Foundation(GrantNo.11326111);Scientific Research Foundation of Heilongjiang Provincial Education Department(Grant No.12541232);Science Research Foundation of Harbin Normal University for Doctor(Grant No.KGB201223);supported by National Science Foundation of China(Grant No.11071051);Natural Science Foundation of Heilongjiang Province(Grant No.A201106);supported by NaturalScience Major Program of Higher Educational Science and Technology Program of Inner Mongolia(Grant No.NJZZ12231)

摘  要:In this paper, the perturbations of the Moore-Penrose metric generalized inverses of linear operators in Banach spaces are described. The Moore Penrose metric generalized inverse is homo- geneous and nonlinear in general, and the proofs of our results are different from linear generalized inverses. By using the quasi-additivity of Moore-Penrose metric generalized inverse and the theorem of generalized orthogonal decomposition, we show some error estimates of perturbations for the single- valued Moore-Penrose metric generalized inverses of bounded linear operators. Furthermore, by means of the continuity of the metric projection operator and the quasi-additivity of Moore-Penrose metric generalized inverse, an expression for Moore-Penrose metric generalized inverse is given.In this paper, the perturbations of the Moore-Penrose metric generalized inverses of linear operators in Banach spaces are described. The Moore Penrose metric generalized inverse is homo- geneous and nonlinear in general, and the proofs of our results are different from linear generalized inverses. By using the quasi-additivity of Moore-Penrose metric generalized inverse and the theorem of generalized orthogonal decomposition, we show some error estimates of perturbations for the single- valued Moore-Penrose metric generalized inverses of bounded linear operators. Furthermore, by means of the continuity of the metric projection operator and the quasi-additivity of Moore-Penrose metric generalized inverse, an expression for Moore-Penrose metric generalized inverse is given.

关 键 词:Banach space Moore-Penrose metric generalized inverse PERTURBATION 

分 类 号:O177.1[理学—数学]

 

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