Naimark's problem
http://dbpedia.org/resource/Naimark's_problem an entity of type: WikicatConjectures
Naimark's problem is a question in functional analysis asked by Naimark. 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. Whether Naimark's problem itself is independent of remains unknown.
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Naimark's problem
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Naimark's problem is a question in functional analysis asked by Naimark. 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.
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