Nonseparable UHF algebras I: Dixmier's problem

Ilijas Farah, Takeshi Katsura

研究成果: Article査読

25 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1399-1430
ページ数32
ジャーナルAdvances in Mathematics
225
3
DOI
出版ステータスPublished - 2010 10

ASJC Scopus subject areas

  • 数学 (全般)

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