One-sided Drazin inverses in Banach algebras and perturbations of B-Fredholm spectra

The famous Drazin inverse and generalized Drazin inverse were introduced by Drazin in 1958 and Koliha in 1996, respectively. In the present paper, the author introduces the concepts of left and right (generalized) Drazin inverses, which are the one-sided versions of classical (generalized) Drazin inverses, in Banach algebras. Several characterizations of one-sided (generalized) Drazin invertible operators on Banach spaces are given. By utilizing the one-sided Drazin invertible spectra, the characterizations of B-Fredholm spectra for Banach space operators are obtained. These perturbational results can be regarded as generalizations of classical Fredholm theory in Banach spaces.