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 gene...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.展开更多
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)+3 种基金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)
文摘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.
