A similarity degree characterization of nuclear $C^*$-algebras
| dc.creator | Pisier, Gilles | |
| dc.date | 2004-09-06 | |
| dc.date | 2005-04-07 | |
| dc.date.accessioned | 2026-07-07T05:11:51Z | |
| dc.date.available | 2026-07-07T05:11:51Z | |
| dc.description | We show that a $C^*$-algebra $A$ is nuclear iff there is a constant $K$ and $α<3$ such that, for any bounded homomorphism $u\colon A \to B(H)$, there is an isomorphism $ξ\colon H\to H$ satisfying $\|ξ^{-1}\|\|ξ\| \le K\|u\|^α$ and such that $ ξ^{-1} u(.) ξ$ is a $*$-homomorphism. In other words, an infinite dimensional $A$ is nuclear iff its length (in ths sense of our previous work on the Kadison similarity problem) is equal to 2. | |
| dc.description | This latest version has minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0409091 | |
| dc.identifier | http://arxiv.org/abs/math/0409091 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72383 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L06,46L07 | |
| dc.title | A similarity degree characterization of nuclear $C^*$-algebras | |
| dc.type | text |