Naimark's problem is a question in functional analysis asked by . It asks whether every C*-algebra that has only one * -representation up to unitary equivalence is isomorphic-algebra of compact operatorss 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 diamond principle to construct a C*-algebra elements is independent of the axioms of Zermelo–Fraenkel set theory and the axiom of choice).

remains unknown.

See also

• \mathsf{ZFC}

• Gelfand–Naimark theorem

References