On the spectral identities and fundamental properties of one-sided Drazin inverses in Banach algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916708982194176 |
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| author | Yan, Kai |
| author_facet | Yan, Kai |
| contents | We establish several fundamental properties of one-sided (generalized) Drazin inverses in Banach algebras, including intertwining properties and reverse order laws. In particular, we introduce the concepts of one-sided strongly pi-regularity, which is shown to be equivalent to one-sided Drazin invertibility. By utilizing the Jacobson's lemma for one-sided regularity, we prove the Jacobson's lemma for one-sided (generalized) Drazin invertibility. These results allow us to derive the spectral identities for one-sided (generalized) Drazin invertible spectra in Banach algebras, as well as the spectral identities for Fredholm type operators acting on Banach spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18995 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the spectral identities and fundamental properties of one-sided Drazin inverses in Banach algebras Yan, Kai Functional Analysis 15A09, 16U99, 47A05 We establish several fundamental properties of one-sided (generalized) Drazin inverses in Banach algebras, including intertwining properties and reverse order laws. In particular, we introduce the concepts of one-sided strongly pi-regularity, which is shown to be equivalent to one-sided Drazin invertibility. By utilizing the Jacobson's lemma for one-sided regularity, we prove the Jacobson's lemma for one-sided (generalized) Drazin invertibility. These results allow us to derive the spectral identities for one-sided (generalized) Drazin invertible spectra in Banach algebras, as well as the spectral identities for Fredholm type operators acting on Banach spaces. |
| title | On the spectral identities and fundamental properties of one-sided Drazin inverses in Banach algebras |
| topic | Functional Analysis 15A09, 16U99, 47A05 |
| url | https://arxiv.org/abs/2504.18995 |