The $\ell ^{1}$-index of Tsirelson type spaces
| dc.creator | Leung, Denny H. | |
| dc.creator | Tang, Wee-Kee | |
| dc.date | 2001-02-22 | |
| dc.date.accessioned | 2026-07-07T04:40:18Z | |
| dc.date.available | 2026-07-07T04:40:18Z | |
| dc.description | If αand βare countable ordinals such that β\neq 0, denote by \tilde{T}_{α,β} the completion of $c_{00}$ with respect to the implicitly defined norm ||x|| = max{||x||_{c_{0}}, 1/2 sup \sum_{i=1}^{j}||E_{i}x||}, where the supremum is taken over all finite subsets E_{1},...,E_{j} of $\mathbb{N}$ such that $E_{1}<...<E_{j}$ and {min E_{1},...,min E_{j}} \in S_β. It is shown that the Bourgain $\ell^{1}$-index of \tilde{T}_{α,β} is ω^{α+β.ω}. In particular, if α=ω^{α_{1}}. m_{1}+...+ω^{α_{n}}. m_{n} in Cantor normal form and α_{n} is not a limit ordinal, then there exists a Banach space whose \ell^{1}-index is ω^α. | |
| dc.identifier | https://arxiv.org/abs/math/0102175 | |
| dc.identifier | http://arxiv.org/abs/math/0102175 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60988 | |
| dc.subject | Functional Analysis | |
| dc.title | The $\ell ^{1}$-index of Tsirelson type spaces | |
| dc.type | text |