Nonseparable UHF algebras I: Dixmier's problem

作者：Farah Ilijas^*; Katsura Takeshi

来源：Advances in Mathematics, 2010, 225(3): 1399-1430.

DOI：10.1016/j.aim.2010.04.006

• Nonseparable
• C*-algebras
• UHF algebras

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.

• 出版日期2010-10-20