Perturbation of the Moore-Penrose metric generalized inverse in reflexive strictly convex Banach spaces.

Let X, Y be reflexive strictly convex Banach spaces, let T, δT: X → Y be bounded linear operators with closed range R( T). Put $$\overline T = T + \delta T$$. In this paper, by using the concept of quasiadditivity and the so called generalized Neumman lemma, we will give some error estimates of the bounds of $$\left\| {{{\overline T }^M}} \right\|$$. By using a relation between the concepts of the reduced minimum module and the gap of two subspaces, some new existence characterization of the Moore-Penrose metric generalized inverse $${\overline T ^M}$$ of the perturbed operator $$\overline T $$ will be also given. [ABSTRACT FROM AUTHOR]