A Note on Approximate Liftings
| dc.creator | Hadwin, Don | |
| dc.creator | Li, Weihua | |
| dc.date | 2008-04-09 | |
| dc.date.accessioned | 2026-07-07T09:31:16Z | |
| dc.date.available | 2026-07-07T09:31:16Z | |
| dc.description | In this paper, we prove approximate lifting results in the C$^{\ast}$-algebra and von Neumann algebra settings. In the C$^{\ast}$-algebra setting, we show that two (weakly) semiprojective unital C*-algebras, each generated by $n$ projections, can be glued together with partial isometries to define a larger (weakly) semiprojective algebra. In the von Neumann algebra setting, we prove lifting theorems for trace-preserving *-homomorphisms from abelian von Neumann algebras or hyperfinite von Neumann algebras into ultraproducts. We also extend a classical result of S. Sakai \cite{sakai} by showing that a tracial ultraproduct of C*-algebras is a von Neumann algebra, which yields a generalization of Lin's theorem \cite{Lin} on almost commuting selfadjoint operators with respect to $\Vert\cdot\Vert_{p}$ on any unital C*-algebra with trace. | |
| dc.identifier | https://arxiv.org/abs/0804.1387 | |
| dc.identifier | http://arxiv.org/abs/0804.1387 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158399 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L05, 46L10 | |
| dc.title | A Note on Approximate Liftings | |
| dc.type | text |