Classification of hyperfinite factors up to completely bounded isomorphism of their preduals
| dc.creator | Haagerup, Uffe | |
| dc.creator | Musat, Magdalena | |
| dc.date | 2007-06-23 | |
| dc.date | 2007-08-08 | |
| dc.date.accessioned | 2026-07-07T08:22:43Z | |
| dc.date.available | 2026-07-07T08:22:43Z | |
| dc.description | In this paper we consider the following problem: When are the preduals of two hyperfinite (=injective) factors $\M$ and $\N$ (on separable Hilbert spaces) cb-isomorphic (i.e., isomorphic as operator spaces)? We show that if $\M$ is semifinite and $\N$ is type III, then their preduals are not cb-isomorphic. Moreover, we construct a one-parameter family of hyperfinite type III$_0$-factors with mutually non cb-isomorphic preduals, and we give a characterization of those hyperfinite factors $\M$ whose preduals are cb-isomorphic to the predual of the unique hyperfinite type III$_1$-factor. In contrast, Christensen and Sinclair proved in 1989 that all infinite dimensional hyperfinite factors with separable preduals are cb-isomorphic. More recently Rosenthal, Sukochev and the first-named author proved that all hyperfinite type III$_λ$-factors, where $0< λ\leq 1$, have cb-isomorphic preduals. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/0706.3463 | |
| dc.identifier | http://arxiv.org/abs/0706.3463 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135747 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L10, 47L25 | |
| dc.title | Classification of hyperfinite factors up to completely bounded isomorphism of their preduals | |
| dc.type | text |