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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.18678 |
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| _version_ | 1866914730462937088 |
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| author | Alves, Thiago R. Souza, Gustavo C. |
| author_facet | Alves, Thiago R. Souza, Gustavo C. |
| contents | In this article, we address a problem posed by F. Bayart regarding the existence of an infinite-dimensional closed vector subspace (excluding the null operator) within the set of supercyclic operators on Banach spaces. We resolve this problem by establishing the existence of the closed subspace. Furthermore, we prove that the set of supercyclic operators on $\ell_1$ contains, up to the null operator, an isometric copy of $\ell_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18678 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the set of supercyclic operators Alves, Thiago R. Souza, Gustavo C. Functional Analysis In this article, we address a problem posed by F. Bayart regarding the existence of an infinite-dimensional closed vector subspace (excluding the null operator) within the set of supercyclic operators on Banach spaces. We resolve this problem by establishing the existence of the closed subspace. Furthermore, we prove that the set of supercyclic operators on $\ell_1$ contains, up to the null operator, an isometric copy of $\ell_1$. |
| title | On the set of supercyclic operators |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2403.18678 |