ABSTRACT
Let R be any associative ring with unit 1 and suppose that satisfy
we prove that 1−ac is Drazin (respectively, generalized Drazin, pseudo-Drazin) invertible if and only if 1−bd is Drazin (respectively, generalized Drazin, pseudo-Drazin) invertible. In other words, we give an affirmative answer to the conjecture of D. Mosić. Moreover, some applications to Banach algebra elements and Banach space operators are also given.
Acknowledgements
The authors are highly grateful to the referees for constructive comments and careful reading of the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.