The G-Drazin Inverse of an Operator Matrix over Banach Spaces.

Let A be a Banach algebra. An element a ϵ A has generalized Drazin inverse if there exists b ϵ A such that b = bab, ab = ba, a - a²b ϵ Aqnil. New additive results for the generalized Drazin inverse of an operator over a Banach space are presented. we extend the main results of a paper of Shakoor, Yang and Ali from 2013 and of Wang, Huang and Chen from 2017. Appling these results to 2 x 2 operator matrices we also generalize results of a paper of Deng, Cvetković-Ilić and Wei from 2010. [ABSTRACT FROM AUTHOR]