Perturbation of the weighted core–EP inverse
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.
KeywordsPerturbation Weighted core–EP inverse Wg–Drazin inverse Hilbert space
Mathematics Subject Classification47A55; 47A50 65F20
The author is supported by the Ministry of Education, Science and Technological Development, Republic of Serbia, grant no. 174007. The authors is grateful to the referee for careful reading of the paper.