On metric characterizations of tree and fragmentability indices of Banach spaces
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918527756140544 |
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| author | Basset, Estelle Lancien, Gilles Procházka, Antonin |
| author_facet | Basset, Estelle Lancien, Gilles Procházka, Antonin |
| contents | We introduce two ordinal indices that are linear invariants for Banach spaces: the dyadic tree index and the sprawling tree index. We show that they are also bi-Lipschitz invariants. In fact, we characterize their values in terms of sub-Lipschitz embeddability of dyadic or countably branching diamond graphs of ordinal height. We derive applications for separable Banach spaces that are universal for complete countable metric spaces and bi-Lipschitz embeddings. We also discuss the links of these tree indices with classical fragmentability indices of Banach spaces such as the dentabilty, weak fragmentability and Szlenk indices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28311 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On metric characterizations of tree and fragmentability indices of Banach spaces Basset, Estelle Lancien, Gilles Procházka, Antonin Functional Analysis Metric Geometry 46B85, 46B80, 46B20, 46B22, 51F30, 30L05 We introduce two ordinal indices that are linear invariants for Banach spaces: the dyadic tree index and the sprawling tree index. We show that they are also bi-Lipschitz invariants. In fact, we characterize their values in terms of sub-Lipschitz embeddability of dyadic or countably branching diamond graphs of ordinal height. We derive applications for separable Banach spaces that are universal for complete countable metric spaces and bi-Lipschitz embeddings. We also discuss the links of these tree indices with classical fragmentability indices of Banach spaces such as the dentabilty, weak fragmentability and Szlenk indices. |
| title | On metric characterizations of tree and fragmentability indices of Banach spaces |
| topic | Functional Analysis Metric Geometry 46B85, 46B80, 46B20, 46B22, 51F30, 30L05 |
| url | https://arxiv.org/abs/2605.28311 |