A new characterization of generalized Browder's theorem and a Cline's formula for generalized Drazin-meromorphic inverses

Abstract

In this paper, we give a new characterization of generalized Browder's theorem by considering equality between the generalized Drazin-meromorphic Weyl spectrum and the generalized Drazin-meromorphic spectrum. Also, we generalize Cline's formula to the case of generalized Drazin-meromorphic invertibility under the assumption that $A^k{B}^k{A}^k=A^{k+1}$ for some positive integer $k$.

12 pages