Majorizing measures and proportional subsets of bounded orthonormal systems
| dc.creator | Guedon, Olivier | |
| dc.creator | Mendelson, Shahar | |
| dc.creator | Pajor, Alain | |
| dc.creator | Tomczak-Jaegermann, Nicole | |
| dc.date | 2008-01-23 | |
| dc.date.accessioned | 2026-07-07T08:56:04Z | |
| dc.date.available | 2026-07-07T08:56:04Z | |
| dc.description | In this article we prove that for any orthonormal system $(\vphi_j)_{j=1}^n \subset L_2$ that is bounded in $L_{\infty}$, and any $1 < k <n$, there exists a subset $I$ of cardinality greater than $n-k$ such that on $\spa\{\vphi_i\}_{i \in I}$, the $L_1$ norm and the $L_2$ norm are equivalent up to a factor $μ(\log μ)^{5/2}$, where $μ= \sqrt{n/k} \sqrt{\log k}$. The proof is based on a new estimate of the supremum of an empirical process on the unit ball of a Banach space with a good modulus of convexity, via the use of majorizing measures. | |
| dc.identifier | https://arxiv.org/abs/0801.3556 | |
| dc.identifier | http://arxiv.org/abs/0801.3556 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146478 | |
| dc.subject | Functional Analysis | |
| dc.subject | Probability | |
| dc.title | Majorizing measures and proportional subsets of bounded orthonormal systems | |
| dc.type | text |