Naimark's problem
Naimark's problem is a question in functional analysis asked by. It asks whether every C*-algebra that has only one irreducible -representation up to unitary equivalence is isomorphic to the -algebra of compact operators on some Hilbert space.
The problem has been solved in the affirmative for special cases. used the -Principle to construct a C*-algebra with generators that serves as a counterexample to Naimark's Problem. More precisely, they showed that the existence of a counterexample generated by Aleph One| elements is independent of the axioms of Zermelo–Fraenkel set theory and the Axiom of Choice.
Whether Naimark's problem itself is independent of remains unknown.
