A note on the Browder’s theorem and a Cline’s formula for generalized Drazin-$g$-meromorphic inverses

Abstract

In this paper, we give a new characterization of Browder’s theorem by means of the generalized Drazin-$g$-meromorphic Weyl spectrum and the generalized Drazin-$g$-meromorphic spectrum. Also, for operators $A$ and $B$ satisfying $A^kB^kA^k = A^{k+1}$ for some positive integer $k$, we generalize Cline’s formula to the case of generalized Drazin-$g$-meromorphic invertibility