Perturbations and expressions of the Moore--Penrose metric generalized inverses and applications to the stability of some operator equations
For researchers in functional analysis and operator theory, this work offers incremental theoretical extensions to the perturbation theory of generalized inverses in Banach spaces.
The paper studies perturbations and expressions of Moore-Penrose metric generalized inverses for bounded linear operators on Banach spaces, providing equivalent conditions for a simplified expression and applying results to analyze stability of operator equations.
In this paper, the problems of perturbation and expression for the Moore--Penrose metric generalized inverses of bounded linear operators on Banach spaces are further studied. By means of certain geometric assumptions of Banach spaces, we first give some equivalent conditions for the Moore--Penrose metric generalized inverse of perturbed operator to have the simplest expression $T^M(I+ δTT^M)^{-1}$. Then, as an application our results, we investigate the stability of some operator equations in Banach spaces under different type perturbations.