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

The famous Drazin inverse and generalized Drazin inverse were originally introduced by Drazin in 1958 and Koliha in 1996, respectively. In this paper, the author presents simplified notions 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 provided. By utilizing the one-sided Drazin invertible spectra, the characterizations of B-Fredholm spectra for Banach space operators are established. These perturbational results can be viewed as extensions of classical Fredholm theory in the context of Banach spaces.