Absolutely representing systems, uniform smoothness, and type
| dc.creator | Vershynin, R. | |
| dc.date | 1998-04-08 | |
| dc.date.accessioned | 2026-07-07T05:24:21Z | |
| dc.date.available | 2026-07-07T05:24:21Z | |
| dc.description | Absolutely representing system (ARS) in a Banach space $X$ is a set $D \subset X$ such that every vector $x$ in $X$ admits a representation by an absolutely convergent series $x = \sum_i a_i x_i$ with $(a_i)$ reals and $(x_i) \subset D$. We investigate some general properties of ARS. In particular, ARS in uniformly smooth and in B-convex Banach spaces are characterized via $ε$-nets of the unit balls. Every ARS in a B-convex Banach space is quick, i.e. in the representation above one can achieve $\|a_i x_i\| < cq^i\|x\|$, $i=1,2,...$ for some constants $c>0$ and $q \in (0,1)$. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/9804044 | |
| dc.identifier | http://arxiv.org/abs/math/9804044 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76806 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B03; 46B07; 52A21 | |
| dc.title | Absolutely representing systems, uniform smoothness, and type | |
| dc.type | text |