A Note on Approximate Liftings

dc.creatorHadwin, Don
dc.creatorLi, Weihua
dc.date2008-04-09
dc.date.accessioned2026-07-07T09:31:16Z
dc.date.available2026-07-07T09:31:16Z
dc.descriptionIn 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.identifierhttps://arxiv.org/abs/0804.1387
dc.identifierhttp://arxiv.org/abs/0804.1387
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158399
dc.subjectOperator Algebras
dc.subject46L05, 46L10
dc.titleA Note on Approximate Liftings
dc.typetext

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