OpenAI research collection · 1 manuscript · Source checked 2026-10-19
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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We construct in ZFC a unital infinite-dimensional simple complex C^(∗)-algebra with a faithful tracial state whose nonzero irreducible representations are all unitarily equivalent. This gives a negative answer to Naimark's problem without additional set-theoretic assumptions.
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