Perturbation analysis for the Moore–Penrose metric generalized inverse of closed linear operators in Banach spaces

Abstract

In this paper, we characterize the perturbations of the Moore–Penrose metric generalized inverse of closed operator in Banach spaces. Under the condition $R\left(\delta T\right)\subset R\left(T\right)$, $N\left(T\right)\subset N\left(\delta T\right)$, respectively, we get some new results about upper-bound estimates of $\Vert {\overline{T}}^M\Vert$ and $\Vert {\overline{T}}^M-T^M\Vert$.