Additive Properties of the generalized and pseudo n-strong Drazin Inverse in Banach Algebras

Rounak Biswas () and Falguni Roy ()
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Rounak Biswas: National Institute of Technology Karnataka
Falguni Roy: National Institute of Technology Karnataka

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 917-929

Abstract: Abstract In this paper, we establish some necessary and sufficient conditions for generalized n-strong Drazin invertibility (gns-invertibility) and pseudo n-strong Drazin invertibility (pns-invertibility) of an element in a Banach algebra for $$n\in {\mathbb {N}}$$ n ∈ N . Subsequently, these results are utilized to prove some additive properties of gns (pns)-Drazin inverse. This process produces a generalization of some recent results of H Chen, M Sheibani (Linear and Multilinear Algebra 70.1 (2022): 53-65) for gns and pns-Drazin inverse.

Keywords: Additive property; gns-Drazin inverse; pns-Drazin inverse; Jacobson radical; 15A09; 47L99; 16N20 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-025-00811-8

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