Additive properties of g-Drazin invertible linear operators

Abstract

In this paper, we investigate additive properties of generalized Drazin inverse for bounded linear operators. As an application we present new conditions under which a $2\times 2$ operator matrix has g-Drazin inverse. These extend the main results of Dana and Yousefi (Int. J. Appl. Comput. Math., {\bf 4}(2018), page 9), Yang and Liu (J. Comput. Appl. Math., {\bf 235}(2011), 1412--1417) and Sun et al. (Filomat, {\bf 30}(2016), 3377--3388).