Isometric rigidity and Fraïssé properties of Orlicz sequence spaces
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918425613303808 |
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| author | de Rancourt, Noé Fakhoury, Micheline |
| author_facet | de Rancourt, Noé Fakhoury, Micheline |
| contents | We provide an approximate version of a rigidity result by Randrianantoanina: for a large class of Orlicz sequence spaces, almost isometric embeddings almost preserve disjointness. In specific cases, we can even prove that such embeddings almost preserve basic vectors. As a consequence, we prove that some Orlicz sequences spaces are guarded Fraïssé but not $ω$-categorical; moreover, they do not contain copies of $\ell_2$ and their age is not closed. This answers a question of Cúth-de Rancourt-Doucha. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_02080 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Isometric rigidity and Fraïssé properties of Orlicz sequence spaces de Rancourt, Noé Fakhoury, Micheline Functional Analysis 46B04 (Primary) 46B45, 46E30, 03C66, 03C35 (Secondary) We provide an approximate version of a rigidity result by Randrianantoanina: for a large class of Orlicz sequence spaces, almost isometric embeddings almost preserve disjointness. In specific cases, we can even prove that such embeddings almost preserve basic vectors. As a consequence, we prove that some Orlicz sequences spaces are guarded Fraïssé but not $ω$-categorical; moreover, they do not contain copies of $\ell_2$ and their age is not closed. This answers a question of Cúth-de Rancourt-Doucha. |
| title | Isometric rigidity and Fraïssé properties of Orlicz sequence spaces |
| topic | Functional Analysis 46B04 (Primary) 46B45, 46E30, 03C66, 03C35 (Secondary) |
| url | https://arxiv.org/abs/2604.02080 |