On the basic sequence structure of variable exponent Lebesgue spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909973659779072 |
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| author | Ansorena, José L. Bello, Glenier |
| author_facet | Ansorena, José L. Bello, Glenier |
| contents | We study the subsymmetric basic sequence structure of variable exponent Lebesgue spaces $L_{P}$ built from index functions $P\colonΩ\to(0,\infty]$ on $σ$-finite measure spaces $(Ω,Σ,μ)$. Specifically, we prove that if $P$ is bounded away from infinity, then any complemented subsymmetric basic sequence of $L_{P}$ is equivalent to the canonical basis of $\ell_r$ for some $r\ge 1$ in the essential range of $P$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19538 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the basic sequence structure of variable exponent Lebesgue spaces Ansorena, José L. Bello, Glenier Functional Analysis We study the subsymmetric basic sequence structure of variable exponent Lebesgue spaces $L_{P}$ built from index functions $P\colonΩ\to(0,\infty]$ on $σ$-finite measure spaces $(Ω,Σ,μ)$. Specifically, we prove that if $P$ is bounded away from infinity, then any complemented subsymmetric basic sequence of $L_{P}$ is equivalent to the canonical basis of $\ell_r$ for some $r\ge 1$ in the essential range of $P$. |
| title | On the basic sequence structure of variable exponent Lebesgue spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2512.19538 |