Additive results for the generalized Drazin inverse
Dragan S. Djordjević, Yimin Wei · Journal of the Australian Mathematical Society · 2002
Abstract Additive perturbation results for the generalized Drazin inverse of Banach space operators are presented. Precisely, ifAddenotes the generalized Drazin inverse of a bounded linear operatorAon an arbitrary complex Banach space, then in some special cases(A + B)dis computed in terms ofAdandBd. Thus, recent results of Hartwig, Wang and Wei (Linear Algebra Appl.322 (2001), 207–217) are extended to infinite dimensional settings with simplified proofs.