B-convex operator spaces
| dc.creator | Parcet, Javier | |
| dc.date | 2003-12-11 | |
| dc.date.accessioned | 2026-07-07T05:03:50Z | |
| dc.date.available | 2026-07-07T05:03:50Z | |
| dc.description | The notion of B-convexity for operator spaces, which a priori depends on a set of parameters indexed by $Σ$, is defined. Some of the classical characterizations of this geometric notion for Banach spaces are studied in this new context. For instance, an operator space is $B_Σ$-convex if and only if it has $Σ$-subtype. The class of uniformly non-$L^1(Σ)$ operator spaces, which is also the class of $B_Σ$-convex operator spaces, is introduced. Moreover, an operator space having non-trivial $Σ$-type is $B_Σ$-convex. However, the converse is false. The row and column operator spaces are nice counterexamples of this fact, since both are Hilbertian. In particular, this result shows that a version of the Maurey-Pisier theorem does not hold in our context. Some other examples of Hilbertian operator spaces will be treated. In the last part of this paper, the independence of $B_Σ$-convexity with respect to $Σ$ is studied. This provides some interesting problems which will be posed. | |
| dc.description | To appear in Proc. Edinburgh Math. Soc. 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0312246 | |
| dc.identifier | http://arxiv.org/abs/math/0312246 | |
| dc.identifier | Proc. Edinburgh Math. Soc. 46 (2003), 649-668. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69575 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L07; 42C15 | |
| dc.title | B-convex operator spaces | |
| dc.type | text |