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 ? 2 operator matrix has g-Drazin inverse. These extend the main results of Dana and Yousefi (Int. J. Appl. Comput. Math., 4(2018), page 9), Yang and Liu (J. Comput. Appl. Math., 235(2011), 1412-1417) and Sun et al. (Filomat, 30(2016), 3377-3388).