Banach空间中线性算子Moore-Penrose度量广义逆的扰动

Perturbation of Moore-Penrose Metric Generalized Inverse of Linear Operators in Banach Space

应用度量稳定扰动的定义及广义正交分解定理,给出在一般范数下有界线性算子的Moore-Penrose单值度量广义逆的误差界估计,并推导出其度量广义逆扰动的范数估计.因为度量广义逆一般为有界齐性的非线性算子,所以其扰动定理的证明与线性广义逆的扰动定理完全不同.

We apply the definition of stable perturbation and generalized orthogonal decomposition theorem to give the Moore-Penrose metric generalized inverse error bound estimate under normal norm,and derive the norm estimate of the perturbation of Moore-Penrose metric generalized inverse.Because the Moore-Penrose metric generalized inverse is a bounded homogeneous nonlinear operator in general,the proof of its perturbation theorem and linear generalized inverse perturbation theorem is completely different.