Perturbation of the weighted core–EP inverse

Abstract

We obtain two different expressions for the weighted core–EP inverse of the sum $$A+E$$ for a given operator A and a perturbation operator E, under different conditions on the perturbing operator. As a consequence of these results, we get some relations between idempotents determined by the weighted core–EP inverses of a given operator and its perturbation and we present perturbation bounds for the weighted core–EP inverse. The application to the solution of a perturbed equation is given. We also apply these results to obtain perturbation results for the core–EP inverse.