The generalized and pseudo $n$-strong Drazin inverse of the sum of elements in Banach algebras
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| Format: | Preprint |
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2025
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| _version_ | 1866909636794253312 |
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| author | Biswas, Rounak Roy, Falguni |
| author_facet | Biswas, Rounak Roy, Falguni |
| contents | In this paper, we begin by introducing some necessary and sufficient conditions for generalized $n$-strong Drazin invertibility (g$n$s-invertibility) and pseudo $n$-strong Drazin invertibility (p$n$s-invertibility) of an element in a Banach algebra for $n\in\mathbb{N}$. Subsequently, these results are utilized to prove some additive properties of g$n$s (p$n$s)-Drazin inverse in a Banach algebra. This process produces a generalization of some recent results of H Chen, M Sheibani (Linear and Multilinear Algebra \textbf{70.1} (2022): 53-65) for g$n$s and p$n$s-Drazin inverse. Furthermore, we define and characterize weighted g$n$s and weighted p$n$s-Drazin inverse in a Banach algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03845 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The generalized and pseudo $n$-strong Drazin inverse of the sum of elements in Banach algebras Biswas, Rounak Roy, Falguni Functional Analysis In this paper, we begin by introducing some necessary and sufficient conditions for generalized $n$-strong Drazin invertibility (g$n$s-invertibility) and pseudo $n$-strong Drazin invertibility (p$n$s-invertibility) of an element in a Banach algebra for $n\in\mathbb{N}$. Subsequently, these results are utilized to prove some additive properties of g$n$s (p$n$s)-Drazin inverse in a Banach algebra. This process produces a generalization of some recent results of H Chen, M Sheibani (Linear and Multilinear Algebra \textbf{70.1} (2022): 53-65) for g$n$s and p$n$s-Drazin inverse. Furthermore, we define and characterize weighted g$n$s and weighted p$n$s-Drazin inverse in a Banach algebra. |
| title | The generalized and pseudo $n$-strong Drazin inverse of the sum of elements in Banach algebras |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2506.03845 |