B-Fredholm theory in Banach algebras
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917580323684352 |
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| author | Zhang, Yunnan Zeng, Qingping Wu, Zhenying |
| author_facet | Zhang, Yunnan Zeng, Qingping Wu, Zhenying |
| contents | The aim of this paper is to develop a systematic B-Fredholm theory in semiprime Banach algebras. We first generalize Smyth's important punctured neighbourhood theorem to B-Fredholm elements. Then using this result, we investigate the local spectral theory of B-Fredholm elements, including the localized left (resp. right) SVEP and a classification of components of B-Fredholm resolvent set. Finally, in semisimple Banach algebra context, we characterize element $f$ such that $f^{n}$ belongs to the socle for some $n \in \mathbb{N}$ from two different perspectives: one is the invariance of the B-Fredholm spectrum under commuting perturbation $f$, the other is the Rieszness and the B-Fredholmness of $f$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | B-Fredholm theory in Banach algebras Zhang, Yunnan Zeng, Qingping Wu, Zhenying Functional Analysis Primary 46H05, 46H10, Secondary 47A53, 47A55 The aim of this paper is to develop a systematic B-Fredholm theory in semiprime Banach algebras. We first generalize Smyth's important punctured neighbourhood theorem to B-Fredholm elements. Then using this result, we investigate the local spectral theory of B-Fredholm elements, including the localized left (resp. right) SVEP and a classification of components of B-Fredholm resolvent set. Finally, in semisimple Banach algebra context, we characterize element $f$ such that $f^{n}$ belongs to the socle for some $n \in \mathbb{N}$ from two different perspectives: one is the invariance of the B-Fredholm spectrum under commuting perturbation $f$, the other is the Rieszness and the B-Fredholmness of $f$. |
| title | B-Fredholm theory in Banach algebras |
| topic | Functional Analysis Primary 46H05, 46H10, Secondary 47A53, 47A55 |
| url | https://arxiv.org/abs/2402.00574 |