On Sequences with at Most a Finite Number of Zero Coordinates
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916286898896896 |
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| author | Alves, Diego Ribeiro, Geivison |
| author_facet | Alves, Diego Ribeiro, Geivison |
| contents | In this paper, we analyze the existence of algebraic and topological structures in the set of sequences that contain only a finite number of zero coordinates. Inspired by the work of Daniel Cariello and Juan B. Seoane-Sepúlveda, our research reveals new insights and complements their notable results beyond the classical \( \ell_p \) spaces for \( p \) in the interval from 1 to infinity, including the intriguing case where \( p \) is between 0 and 1.
Our exploration employs notions such as S-lineability, pointwise lineability, and (alpha, beta)-spaceability. This investigation allowed us to verify, for instance, that the set \( F \setminus Z(F) \), where \( F \) is a closed subspace of \( \ell_p \) containing \( c_0 \), is (alpha, c)-spaceable if and only if alpha is finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06859 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Sequences with at Most a Finite Number of Zero Coordinates Alves, Diego Ribeiro, Geivison Functional Analysis In this paper, we analyze the existence of algebraic and topological structures in the set of sequences that contain only a finite number of zero coordinates. Inspired by the work of Daniel Cariello and Juan B. Seoane-Sepúlveda, our research reveals new insights and complements their notable results beyond the classical \( \ell_p \) spaces for \( p \) in the interval from 1 to infinity, including the intriguing case where \( p \) is between 0 and 1. Our exploration employs notions such as S-lineability, pointwise lineability, and (alpha, beta)-spaceability. This investigation allowed us to verify, for instance, that the set \( F \setminus Z(F) \), where \( F \) is a closed subspace of \( \ell_p \) containing \( c_0 \), is (alpha, c)-spaceable if and only if alpha is finite. |
| title | On Sequences with at Most a Finite Number of Zero Coordinates |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2406.06859 |