Perturbation analysis for the Moore--Penrose metric generalized inverse of bounded linear operators

Abstract

Utilizing the gap between homogenous subsets which is introduced in this paper, the perturbations for the Moore--Penrose metric generalized inverses of bounded linear operators in Banach spaces are discussed. Under range--preseving, kernel--preseving and general case, respectively, we get some new results about error estimate of the perturbations for the Moore--Penrose metric generalized inverse of bounded linear operators.