Algebra · Oct 6, 2026
A ZFC counterexample to Naimark's problem
Gives an alternative to [Tanaka's ZFC construction](https://arxiv.org/abs/2609.26930v1) of a unital infinite-dimensional simple complex C∗-algebra with a faithful tracial state and exactly one nonzero irreducible representation up to unitary equivalence. Thus the unrestricted compact-operator characterization fails without additional set-theoretic assumptions; the counterexample is nonseparable.
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