The generalized and pseudo n-strong Drazin inverse of the sum of elements in Banach algebras

2025/06/04 by Biswas, Rounak, Roy, Falguni
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2506.03845

Abstract

In this paper, we begin by introducing 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∈ℕ. Subsequently, these results are utilized to prove some additive properties of gns (pns)-Drazin inverse in a Banach algebra. 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. Furthermore, we define and characterize weighted gns and weighted pns-Drazin inverse in a Banach algebra.

Citations

• Generalized Hirano inverses in rings
• Nil clean rings
• Pseudo-Inverses in Associative Rings and Semigroups

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