Embedding of the operator space OH and the logarithmic `little Grothendieck inequality'
| dc.creator | Junge, Marius | |
| dc.date | 2003-05-27 | |
| dc.date.accessioned | 2026-07-07T04:58:19Z | |
| dc.date.available | 2026-07-07T04:58:19Z | |
| dc.description | Using free random varaibles we find an embedding of the operator space $OH$ in the predual of a von Neumann algebra. The properties of this embedding allow us to determined the projection constant of $OH_n$, i.e. there exists a projection $P:B(\ell_2)\to OH_n$ whose completely bounded norm behaves as n^{1/2}/(1+ln n)^{1/2}. According to recent results of Pisier/Shlyahtenko, the lower bound holds for every projection. Improving a previous estimate of order $(1+ ln n)$ of the author, Pisier/Shlyahtenko obtained a `logarithmic little Grothendieck inequality'. We find a second proof of this inequality which explains why the factor $\sqrt{1+\ln n}$ is indeed necessary. In particular the operator space version of the `little Grothendieck inequality' fails to hold. This `logarithmic little Grothendieck' inequality characterizes $C^*$-algebras with the weak expectation property of Lance. | |
| dc.identifier | https://arxiv.org/abs/math/0305387 | |
| dc.identifier | http://arxiv.org/abs/math/0305387 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67589 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 47L25,46L53, 46L54 | |
| dc.title | Embedding of the operator space OH and the logarithmic `little Grothendieck inequality' | |
| dc.type | text |