Nonseparable UHF algebras I: Dixmier's problem

Details Nonseparable UHF algebras I: Dixmier's problem Nonseparable UHF algebras I: Dixmier's problem

2009-06-08

arxiv.org/abs/0906.1401v2

Mathematics

Operator Algebras

To appear in Adv. Math

Scientific paper

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.

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