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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Naimark problem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11411906 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Naimark problem Context triple: [Mark Naimark, hasTheoremNamedAfter, Naimark problem]
-
A.
Steklov eigenvalue problem
The Steklov eigenvalue problem is a type of spectral boundary value problem in which eigenvalues appear in the boundary conditions of a partial differential equation, playing a key role in mathematical physics and geometric analysis.
-
B.
Sturm–Liouville problem
The Sturm–Liouville problem is a class of second-order linear differential equations with boundary conditions that yield real eigenvalues and orthogonal eigenfunctions forming a basis for function expansions in mathematical physics and engineering.
-
C.
Bohr–Courant theorem
The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.
-
D.
Dirichlet problem
The Dirichlet problem is a fundamental boundary value problem in potential theory and partial differential equations, asking for a function that solves a specified PDE inside a domain while taking prescribed values on the domain’s boundary.
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E.
Gelfand–Levitan theory
Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Naimark problem Target entity description: 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.
-
A.
Steklov eigenvalue problem
The Steklov eigenvalue problem is a type of spectral boundary value problem in which eigenvalues appear in the boundary conditions of a partial differential equation, playing a key role in mathematical physics and geometric analysis.
-
B.
Sturm–Liouville problem
The Sturm–Liouville problem is a class of second-order linear differential equations with boundary conditions that yield real eigenvalues and orthogonal eigenfunctions forming a basis for function expansions in mathematical physics and engineering.
-
C.
Bohr–Courant theorem
The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.
-
D.
Dirichlet problem
The Dirichlet problem is a fundamental boundary value problem in potential theory and partial differential equations, asking for a function that solves a specified PDE inside a domain while taking prescribed values on the domain’s boundary.
-
E.
Gelfand–Levitan theory
Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
- F. None of above. chosen
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 ⓘ |
| 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 ⓘ |
| 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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Naimark problem Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.