Resumen de New extensions of Cline's formula for generalized Drazin–Riesz inverses

Abdelaziz Tajmouati, Mohammed Karmouni, M. B. Mohamed Ahmed

• In this note, Cline’s formula for generalized Drazin–Riesz inverses is proved. We prove that if A, D ∈ B(X, Y ) and B, C ∈ B(Y, X) are such that ACD = DBD and DBA = ACA, then AC is generalized Drazin–Riesz invertible if and only if BD is generalized Drazin–Riesz invertible, and that, in such a case, if S is a generalized Drazin–Riesz inverse of AC then T := BS₂D is a generalized Drazin–Riesz inverse of BD.