About: 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. Whether Naimark's problem itself is independent of remains unknown.

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rdfs:label	Naimark's problem (en)
rdfs:comment	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. (en)
dcterms:subject	Conjectures Unsolved problems in mathematics Independence results C*-algebras
Wikipage page ID	1732798 (xsd:integer)
Wikipage revision ID	1096576349 (xsd:integer)
Link from a Wikipage to another Wikipage	Aleph One Conjectures Unsolved problems in mathematics Gelfand–Naimark theorem Proceedings of the National Academy of Sciences Independence results Compact operator on Hilbert space Zermelo–Fraenkel set theory Functional analysis Irreducible representation Hilbert space Isomorphic C-algebras Diamond principle Axiom of choice C-algebra Self-adjoint operator List of statements undecidable in ZFC
sameAs	Naimark's problem Naimark's problem Naimark's problem Naimark's problem
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has abstract	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. (en)
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foaf:isPrimaryTopicOf	wikipedia-en:Naimark's_problem
is Link from a Wikipage to another Wikipage of	Naimark List of Russian mathematicians List of Russian scientists Diamond principle Mark Naimark List of statements independent of ZFC Naimark problem
is Wikipage redirect of	Naimark problem
is Wikipage disambiguates of	Naimark
is foaf:primaryTopic of	wikipedia-en:Naimark's_problem

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