ABSTRACT
Let be a complex Banach algebra. An element
has g-Drazin inverse if there exists
such that
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).
Acknowledgments
The authors would like to thank the referee for his/her helpful suggestions for the improvement of this paper. The very detailed comments improve many proofs of the paper, e.g. Theorem 3.5.
Disclosure statement
No potential conflict of interest was reported by the authors.