Naimark's problem
In mathematics, 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). In 2003 Charles Akemann and Nik Weaver showed that the statement "there exists a counterexample to Naimark's problem which is generated by &alefsym1 elements" is independent of the axioms of Zermelo-Fraenkel set theory and the axiom of choice (ZFC).
See alsoList of statements undecidable in ZFCGel'fand-Naimark theorem
External linkAkemann, C., and N. Weaver, Consistency of a counterexample to Naimark's problem e-print
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