Remarks on the point character of Banach spaces and non-linear embeddings into~$c_0(\Ga)$
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910285303906304 |
|---|---|
| author | Hajek, Petr Johanis, Michal Schlumprecht, Th. |
| author_facet | Hajek, Petr Johanis, Michal Schlumprecht, Th. |
| contents | We give a brief survey of the results on coarse or uniform embeddings of Banach spaces into $c_0(\Ga)$ and the point character of Banach spaces. In the process we prove several new results in this direction (for example we determine the point character of the spaces $L_p(μ)$, $1\le p\le2$) solving open problems posed by C.~Avart, P.~Komjath, and V.~Roedl and by G.~Godefroy, G.~Lancien, and V.~Zizler. In particular, we show that $X=L_p(μ)$, $1\le p<\infty$, bi-Lipschitz embeds into $c_0(\Ga)$ if and only if $\dens X<\om_\om$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00831 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Remarks on the point character of Banach spaces and non-linear embeddings into~$c_0(\Ga)$ Hajek, Petr Johanis, Michal Schlumprecht, Th. Functional Analysis 46B25, 46B26, 46B80, 54E15, 54F45 We give a brief survey of the results on coarse or uniform embeddings of Banach spaces into $c_0(\Ga)$ and the point character of Banach spaces. In the process we prove several new results in this direction (for example we determine the point character of the spaces $L_p(μ)$, $1\le p\le2$) solving open problems posed by C.~Avart, P.~Komjath, and V.~Roedl and by G.~Godefroy, G.~Lancien, and V.~Zizler. In particular, we show that $X=L_p(μ)$, $1\le p<\infty$, bi-Lipschitz embeds into $c_0(\Ga)$ if and only if $\dens X<\om_\om$. |
| title | Remarks on the point character of Banach spaces and non-linear embeddings into~$c_0(\Ga)$ |
| topic | Functional Analysis 46B25, 46B26, 46B80, 54E15, 54F45 |
| url | https://arxiv.org/abs/2401.00831 |