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Nonseparable UHF algebras I: Dixmier's problem |
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| Authors: | Ilijas Farah Takeshi Katsura |
| Institution: | a Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, Canada, M3J 1P3 b Matematicki Institut, Kneza Mihaila 34, Belgrade, Serbia c Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kouhoku-ku, Yokohama, Japan, 223-8522 |
| 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: | 46L05 03E75 |
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