Abstract and Applied Analysis
Volume 7 (2002), Issue 6, Pages 335-347

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

N. Castro González,1 J. J. Koliha,2 and V. Rakočević3

1Departmento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica de Madrid, Boadilla del Monte, Madrid 28660, Spain
2Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia
3Department of Mathematics, Faculty of Philosophy, University of Niš, Yugoslavia 1800 Niš, Serbia and Montenegro

Received 17 June 2000

Copyright © 2002 N. Castro González et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.