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 (not necessarily separable) Hilbert space. The problem has been solved in the affirmative for special cases (specifically for separable and Type-I C*-algebras). 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 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. See also List of statements undecidable in Gelfand–Naimark Theorem References Conjectures C*-algebras Independence results Unsolved problems in mathematics