One-sided extended g-Drazin inverses

Abstract

The principal goal of this paper is to present one-sided versions of the extended g-Drazin inverse as weaker kinds of the extended g-Drazin inverse. Precisely, we define left and right extended g-Drazin inverses for Banach algebra elements. A number of characterizations for left and right extended g-Drazin inverses are developed. Since we obtain equivalence between concepts of left (or right) extended g-Drazin invertibility and left (or right) generalized Drazin invertibility, in fact, we get new characterizations for left (or right) generalized Drazin invertibility as consequences. As particular cases of one-sided extended g-Drazin inverses, we investigate one-sided extended Drazin inverses.