Authors: Farah, Ilijas 
Katsura, Takeshi
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Nonseparable UHF algebras I: Dixmier's problem
Journal: Advances in Mathematics
Volume: 225
Issue: 3
First page: 1399
Last page: 1430
Issue Date: 1-Oct-2010
Rank: M21a
ISSN: 0001-8708
DOI: 10.1016/j.aim.2010.04.006
Abstract: 
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.
Keywords: C*-algebras | Nonseparable | UHF algebras
Publisher: Elsevier

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