An $\ell^1$-Isometric Subspace of $C[0,1]$ with Countable Oscillating Spectrum
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914072350425088 |
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| author | Ribeiro, Geivison |
| author_facet | Ribeiro, Geivison |
| contents | In this paper we construct a closed subspace $X\subset C[0,1]$ with countable oscillating spectrum $Ω(X)$ such that $X$ is isometric to $\ell^1$. This provides a negative answer to Question~4.3 posed by Enflo, Gurariy, and Seoane in [Trans. Amer. Math. Soc. \textbf{366} (2014)]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26066 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An $\ell^1$-Isometric Subspace of $C[0,1]$ with Countable Oscillating Spectrum Ribeiro, Geivison Functional Analysis 15A03, 26A15, 46E15 In this paper we construct a closed subspace $X\subset C[0,1]$ with countable oscillating spectrum $Ω(X)$ such that $X$ is isometric to $\ell^1$. This provides a negative answer to Question~4.3 posed by Enflo, Gurariy, and Seoane in [Trans. Amer. Math. Soc. \textbf{366} (2014)]. |
| title | An $\ell^1$-Isometric Subspace of $C[0,1]$ with Countable Oscillating Spectrum |
| topic | Functional Analysis 15A03, 26A15, 46E15 |
| url | https://arxiv.org/abs/2509.26066 |