A Cline's formula for the generalized Drazin-Riesz inverses
Abdelaziz Tajmouati · Functional Analysis, Approximation and Computation · 2018
Let X be Banach space, A,B,C be bounded linear operators on X satisfying operator equation ABA = ACA. In this note, we show that AC is generalized Drazin-Riesz invertible if and only if BA is generalized Drazin Riesz invertible. So, we generalize Cline’s formula to the case of the generalized Drazin-Riesz invertibility.