Perturbations of Moore-Penrose metric generalized inverses of linear operators in Banach spaces
Perturbations of Moore-Penrose metric generalized inverses of linear operators in Banach spaces
复制标题
DOI：
10.1007/s10114-014-3340-z
复制
发表时间：
2014-06
期刊：
影响因子：
--
通讯作者：
Haifeng Ma;S. Sun;Yuwen Wang;W. Zheng
中科院分区：
文献类型：
--
作者：
Haifeng Ma;S. Sun;Yuwen Wang;W. Zheng
本文讨论了Banach空间中线性算子的Moore-Penrose度量广义逆的扰动。Moore-Penrose度量广义逆一般是齐次的、非线性的，我们的结果的证明不同于线性广义逆.利用Moore-Penrose度量广义逆的拟可加性和广义正交分解定理，给出了有界线性算子的单值Moore-Penrose度量广义逆扰动的误差估计.利用度量投影算子的连续性和Moore-Penrose度量广义逆的拟可加性，给出了Moore-Penrose度量广义逆的一个表达式.
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.