|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||Nonseparable UHF algebras I: Dixmier's problem||Journal:||Advances in Mathematics||Volume:||225||Issue:||3||First page:||1399||Last page:||1430||Issue Date:||1-Oct-2010||Rank:||M21a||ISSN:||0001-8708||DOI:||10.1016/j.aim.2010.04.006||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:||C*-algebras | Nonseparable | UHF algebras||Publisher:||Elsevier|
Show full item record
checked on Dec 2, 2023
checked on Dec 1, 2023
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.