Abstract
In this paper, we investigate additive properties of generalized Drazin inverse of two Drazin invertible linear operators in Banach spaces. Under the commutative condition of P Q = Q P , we give explicit representations of the generalized Drazin inverse ( P + Q ) d in term of P, P d , Q and Q d . We consider some applications of our results to the perturbation of the Drazin inverse and analyze a number of special cases.
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