Naimark's Problem
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Naimark''s problem is a question in functional analysis. 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 was solved in the affirmative for special cases (separable and type I C -algebras). Akemann & Weaver (2004) used to construct a C -algebra serving as a counterexample to Naimark''s problem and showed that the statement "there exists a counterexample to Naimark''s problem which is generated by 1 elements" is independent of the axioms of Zermelo-Fraenkel...
Naimark''s problem is a question in functional analysis. 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 was solved in the affirmative for special cases (separable and type I C -algebras). Akemann & Weaver (2004) used to construct a C -algebra serving as a counterexample to Naimark''s problem and showed that the statement "there exists a counterexample to Naimark''s problem which is generated by 1 elements" is independent of the axioms of Zermelo-Fraenkel set theory and the axiom of choice (ZFC).
