2009/06/08 by Ilijas Farah, Farah, Ilijas, Takeshi Katsura +1 · 1 citation
Mathematics · #03E75 #46L05 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Logic (math.LO) #Operator Algebras (math.OA) #math.LO #math.OA #msc:03E75 #msc:46L05
paper · pdf · doi:10.48550/arxiv.0906.1401
To appear in Adv. Math
openalex publication_date 2009/06/08 · arxiv created 2010/02/22 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are three natural ways to define UHF (uniformly hyperfinite) C*-algebras, and all three definitions are equivalent for separable algebras. In 1967 Dixmier asked whether the three definitions remain equivalent for not necessarily separable algebras. We give a complete answer to this question. More precisely, we show that in small cardinality two definitions remain equivalent, and give counterexamples in other cases. Our results do not use any additional set-theoretic axioms beyond the usual axioms, namely ZFC.