The g-Drazin inverse of the sum in Banach algebras
Huanyin Chen, Marjan Sheibani · Linear and Multilinear Algebra · 2020
Let A be a complex Banach algebra. An element a∈A has g-Drazin inverse if there exists b∈A such that b=bab,ab=ba,a−a2b∈Aqnil. New additive results for the g-Drazin inverse in a Banach algebra are presented. These extend the main results of Deng and Wei (J. Math. Analysis Appl., 379(2010), 313–321) and Wang et al. (Filomat, 30(2016), 1185–1193).