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

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, Rako ) evi ' 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.

Keywords:

• Drazin Inverse
• Closed Linear Operators
• Perturbation
• Perturbed Linear Equation