2008/04/09 by Don Hadwin, Weihua Li, Hadwin, Don +1 · 1 citation
Mathematics · #46L05 #46L10 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.0804.1387
openalex publication_date 2008/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove approximate lifting results in the C∗-algebra and von Neumann algebra settings. In the C∗-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 \citesakai by showing that a tracial ultraproduct of C*-algebras is a von Neumann algebra, which yields a generalization of Lin's theorem \citeLin on almost commuting selfadjoint operators with respect to \Vert⋅\Vertp on any unital C*-algebra with trace.