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

• Autores: Abdelaziz Tajmouati, Mohammed Karmouni, M. B. Mohamed Ahmed
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 60, Nº. 2, 2019, págs. 567-572
• Idioma: inglés
• DOI: 10.33044/revuma.v60n2a18
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• Resumen

  • 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.

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