The $m$-generalized right group inverses in Banach algebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918091244437504 |
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| author | Chen, Huanyin Sheibani, Marjan |
| author_facet | Chen, Huanyin Sheibani, Marjan |
| contents | In this paper, we introduce the concept of the m-generalized right group inverse. This serves as a natural extension of both the m-weak group inverse and the generalized group inverse. We characterize this new generalized inverse using the m-generalized right group decomposition and a polar-like property. Additionally, we present the representation of the m-generalized right group inverse using the generalized right core inverse, leading to new insights and properties for both the m-weak group inverse and the generalized group inverse. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10600 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $m$-generalized right group inverses in Banach algebras Chen, Huanyin Sheibani, Marjan Rings and Algebras Functional Analysis 15A09, 16U50, 16W10 In this paper, we introduce the concept of the m-generalized right group inverse. This serves as a natural extension of both the m-weak group inverse and the generalized group inverse. We characterize this new generalized inverse using the m-generalized right group decomposition and a polar-like property. Additionally, we present the representation of the m-generalized right group inverse using the generalized right core inverse, leading to new insights and properties for both the m-weak group inverse and the generalized group inverse. |
| title | The $m$-generalized right group inverses in Banach algebras |
| topic | Rings and Algebras Functional Analysis 15A09, 16U50, 16W10 |
| url | https://arxiv.org/abs/2507.10600 |