Abstract and Applied Analysis
Volume 7 (2002), Issue 6, Pages 335-347
doi:10.1155/S1085337502002890

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

N. Castro González1 , J.J. Koliha2 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 Ni {s}, Yugoslavia 1800 Ni {s}, Serbia and Montenegro

Abstract

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.