Unconditional basic sequences in function spaces with applications to Orlicz spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912119982653440 |
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| author | Ansorena, José L. Bello, Glenier |
| author_facet | Ansorena, José L. Bello, Glenier |
| contents | We find conditions on a function space $\bf{L}$ that ensure that it behaves as an $L_p$-space in the sense that any unconditional basis of a complemented subspace of $\bf{L}$ either is equivalent to the unit vector system of $\ell_2$ or has a subbasis equivalent to a disjointly supported basic sequence. This dichotomy allows us to classify the symmetric basic sequences of $\bf{L}$. Several applications to Orlicz function spaces are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unconditional basic sequences in function spaces with applications to Orlicz spaces Ansorena, José L. Bello, Glenier Functional Analysis We find conditions on a function space $\bf{L}$ that ensure that it behaves as an $L_p$-space in the sense that any unconditional basis of a complemented subspace of $\bf{L}$ either is equivalent to the unit vector system of $\ell_2$ or has a subbasis equivalent to a disjointly supported basic sequence. This dichotomy allows us to classify the symmetric basic sequences of $\bf{L}$. Several applications to Orlicz function spaces are provided. |
| title | Unconditional basic sequences in function spaces with applications to Orlicz spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2407.18660 |