Abstract. A bounded linear operator in a Banach space is called Koliha--Drazin invertible (generalized Drazin invertible) if ${0}$ is not an accumulation point of its spectrum. In this paper the main result is the stability of the Koliha--Drazin invertible operators with finite nullity under commuting Riesz operator perturbations. We also generalize some recent results of Castro, Koliha and Wei, and characterize the perturbation of the Koliha--Drazin invertible operators with essentialy equal eigenprojections at zero.

AMS Subject Classification (1991): 47A05, 47A53, 15A09

Keyword(s): generalized Drazin inverse, perturbation, Riesz operator

Received January 2, 2001, and in revised form March 26, 2001. (Registered under 2877/2009.)