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We study perturbations and continuity of the Drazin inverse of a closed linear operator A and obtain explicit error estimates in terms of the gap between closed operators and the gap between ranges and nullspaces of operators. The results are used to derive  a theorem on the continuity of the Drazin inverse for closed operators and to describe the asymptotic behavior of operator semigroups

Continuity and general perturbation of the Drazin inverse for closed linear operators