Nonseparable UHF algebras I: Dixmier's problem

Ilijas Farah, Takeshi Katsura

Research output: Contribution to journalArticle

15 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1399-1430
Number of pages32
JournalAdvances in Mathematics
Volume225
Issue number3
DOIs
Publication statusPublished - 2010 Oct

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Nonseparable
Axioms
Algebra
C*-algebra
Counterexample
Cardinality

Keywords

  • C*-algebras
  • Nonseparable
  • UHF algebras

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Nonseparable UHF algebras I : Dixmier's problem. / Farah, Ilijas; Katsura, Takeshi.

In: Advances in Mathematics, Vol. 225, No. 3, 10.2010, p. 1399-1430.

Research output: Contribution to journalArticle

Farah, Ilijas ; Katsura, Takeshi. / Nonseparable UHF algebras I : Dixmier's problem. In: Advances in Mathematics. 2010 ; Vol. 225, No. 3. pp. 1399-1430.
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