Asymptotic smoothness, concentration properties in Banach spaces and applications
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913582122270720 |
|---|---|
| author | Fovelle, Audrey |
| author_facet | Fovelle, Audrey |
| contents | We prove an optimal result of stability under $\ell_p$-sums of some concentration properties for Lipschitz maps defined on Hamming graphs into Banach spaces. As an application, we give examples of spaces with Szlenk index arbitrarily high that admit nevertheless a concentration property. In particular, we get the very first examples of Banach spaces with concentration but without asymptotic smoothness property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15900 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic smoothness, concentration properties in Banach spaces and applications Fovelle, Audrey Functional Analysis Metric Geometry We prove an optimal result of stability under $\ell_p$-sums of some concentration properties for Lipschitz maps defined on Hamming graphs into Banach spaces. As an application, we give examples of spaces with Szlenk index arbitrarily high that admit nevertheless a concentration property. In particular, we get the very first examples of Banach spaces with concentration but without asymptotic smoothness property. |
| title | Asymptotic smoothness, concentration properties in Banach spaces and applications |
| topic | Functional Analysis Metric Geometry |
| url | https://arxiv.org/abs/2311.15900 |