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On generalized n-strong Drazin-\(\mathcal {R}\) inverses in Banach algebras

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Abstract

Inspired by Mosić (Linear Multilinear Algebra 69(2):361–375, 2021) and Živković-Zlatanović (Linear Multilinear Algebra, 2023. https://doi.org/10.1080/03081087.2023.2181940), this paper aims to introduce generalized n-strong Drazin-\(\mathcal {R}\) invertible elements. Several characterizations are given to detect the so called generalized n-strong Drazin-\(\mathcal {R}\) invertible elements. Also, we extend the Cline’s formula to the context of generalized Drazin-\(\mathcal {R}\) (resp. generalized n-strong Drazin-\(\mathcal {R}\)) invertible elements.

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  1. Department of Mathematics, Dhar El Mahraz Faculty of Sciences, Sidi Mohamed Ben Abdellah University, BO 1796, Fes-Atlas, 30003, Fez, Morocco

    Othman Abad

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  1. Othman Abad
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Correspondence to Othman Abad.

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Abad, O. On generalized n-strong Drazin-\(\mathcal {R}\) inverses in Banach algebras. Rend. Circ. Mat. Palermo, II. Ser (2024). https://doi.org/10.1007/s12215-024-01044-0

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  • DOI: https://doi.org/10.1007/s12215-024-01044-0

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