Trees and Branches in Banach Spaces
| dc.creator | Odell, Edward | |
| dc.creator | Schlumprecht, Thomas | |
| dc.date | 2000-02-25 | |
| dc.date.accessioned | 2026-07-07T04:34:04Z | |
| dc.date.available | 2026-07-07T04:34:04Z | |
| dc.description | An infinite dimensional notion of asymptotic structure is considered. This notion is developed in terms of trees and branches on Banach spaces. Every countably infinite countably branching tree $\mathcal T$ of a certain type on a space X is presumed to have a branch with some property. It is shown that then X can be embedded into a space with an FDD $(E_i)$ so that all normalized sequences in X which are almost a skipped blocking of $(E_i)$ have that property. As an application of our work we prove that if X is a separable reflexive Banach space and for some $1<p<\infty$ and $C<\infty$ every weakly null tree $\mathcal T$ on the sphere of X has a branch C-equivalent to the unit vector basis of $\ell_p$, then for all $ε>0$, there exists a finite codimensional subspace of X which $C^2+ε$ embeds into the $\ell_p$ sum of finite dimensional spaces. | |
| dc.description | LaTeX, 24pp | |
| dc.identifier | https://arxiv.org/abs/math/0002219 | |
| dc.identifier | http://arxiv.org/abs/math/0002219 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58763 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B03, 46B20 | |
| dc.title | Trees and Branches in Banach Spaces | |
| dc.type | text |