Error Bounds for the Perturbation of the Drazin Inverse of Closed Operations with Equal Spectral Projections

Abstract

We study perturbations of the Drazin inverse of a closed linear operator A for the case when the perturbed operator has the same spectral projection as A. This theory subsumes results recently obtained by Wei and Wang, Rakočevič and Wei, and Castro and Koliha. We give explicit error estimates for the perturbation of Drazin inverse, and error estimates involving higher powers of the operators