Naimark problem
E924211
The Naimark problem is a question in operator algebra theory concerning whether every C*-algebra with certain representation properties must be of a particularly well-behaved (type I) form.
Statements (32)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical problem
ⓘ
open problem in operator algebras ⓘ |
| appliesTo | C*-algebras with specified representation properties ⓘ |
| asksWhether |
a C*-algebra whose irreducible representations are all of type I must itself be type I
ⓘ
every C*-algebra with only type I irreducible representations is type I ⓘ |
| concerns |
C*-algebras
ⓘ
representations of C*-algebras ⓘ |
| context |
noncommutative topology
ⓘ
structure theory of C*-algebras ⓘ |
| field |
C*-algebra theory
ⓘ
functional analysis ⓘ operator algebra theory ⓘ |
| hasImplicationFor |
classification of C*-algebras up to *-isomorphism
ⓘ
understanding of primitive ideal spaces of C*-algebras ⓘ |
| hasNegativeAnswer | there exists a C*-algebra all of whose irreducible representations are type I but which is not type I under certain set-theoretic assumptions ⓘ |
| hasNegativeAnswerUnderAssumption |
continuum hypothesis
ⓘ
diamond principle NERFINISHED ⓘ |
| hasSolutionUnderAssumption |
continuum hypothesis
ⓘ
diamond principle ⓘ |
| involvesProperty |
C*-algebra being type I
ⓘ
all irreducible representations are of type I ⓘ |
| isIndependentOf | Zermelo–Fraenkel set theory with the axiom of choice ⓘ |
| isQuestionAbout | relationship between representation type and structural type of C*-algebras ⓘ |
| motivation | classification of C*-algebras by representation type ⓘ |
| namedAfter | Mark Naimark NERFINISHED ⓘ |
| relatedConcept |
irreducible representation
ⓘ
primitive ideal space ⓘ representation theory of C*-algebras ⓘ type I C*-algebra ⓘ |
| relatedTo |
nonseparable C*-algebras
ⓘ
set-theoretic methods in operator algebras ⓘ |
| status | independence result from ZFC ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.