In 1948 Naimark showed that the C*-algebra of compact operators, K(H), has a unique irreducible representation and asked whether the converse is true; that is, must any C*-algebra with this property be isomorphic to K(H)? We will out line the proof of Akemann and Weaver (2003) that the existence of a counterexample to Naimark's Problem is consistent with the axioms of set theory ZFC.
Notes on the relative consistency of Naimark's Problem Sponsored by the Meyer Fund