  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.
