New applications of extremely regular function spaces
| Autor: | Abrahamsen, Trond A., Nygaard, Olav, Põldvere, Märt |
|---|---|
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Pacific J. Math. 301 (2019) 385-394 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/pjm.2019.301.385 |
| Popis: | Let $L$ be an infinite locally compact Hausdorff topological space. We show that extremely regular subspaces of $C_0(L)$ have very strong diameter $2$ properties and, for every real number $\varepsilon$ with $0<\varepsilon<1$, contain an $\varepsilon$-isometric copy of $c_0$. If $L$ does not contain isolated points they even have the Daugavet property, and thus contain an asymptotically isometric copy of $\ell_1$. Comment: 9 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|