| Perturbations of Moore–Penrose Metric Generalized Inverses of Linear Operators in Banach Spaces |
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| 基金项目： | The first author is supported by National Science Foundation of China, Tian Yuan Special Foundation （Grant No. 11326111）, Scientific Research Foundation of Heilongjiang Provincial Education Department （Grant No. 12541232） and Science Research Foundation of Harbin Normal University for Doctor （Grant No. KGB201223）; the third author is supported by National Science Foundation of China （Grant No. 11071051） and Natural Science Foundation of Heilongjiang Province （Grant No. A201106）; the fourth author is supported by Natural Science Major Program of Higher Educational Science and Technology Program of Inner Mongolia （Grant No. NJZZ12231） |
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| 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 homogeneous 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 singlevalued 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.
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| 关 键 词： | Banach空间 度量广义逆 界线性算子 扰动 度量投影算子 交分解定理 误差估计 非线性 |
Perturbations of Moore-Penrose metric generalized inverses of linear operators in Banach spaces |
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| Authors: | Hai Feng Ma Shuang Sun YuWen Wang Wen Jing Zheng |
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| Institution: | 1. School of Mathematical Science, Harbin Normal University, Harbin, 150025, P. R. China
2. Department of Mathematics, Hulunbuir College, Hailar, 021008, P. R. China
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| Abstract: | 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 homogeneous 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. |
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| Keywords: | Banach space Moore-Penrose metric generalized inverse perturbation |
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