Riesz–Thorin interpolation theorem
E746578
The Riesz–Thorin interpolation theorem is a fundamental result in functional analysis that provides bounds for linear operators between Lᵖ spaces by interpolating their behavior between two known endpoint estimates.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Riesz–Thorin interpolation theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8640755 — 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: Riesz–Thorin interpolation theorem Context triple: [Frigyes Riesz, knownFor, Riesz–Thorin interpolation theorem]
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A.
Riesz–Fischer theorem
The Riesz–Fischer theorem is a fundamental result in functional analysis that establishes the equivalence between square-summable sequences and square-integrable functions, providing the foundation for the Hilbert space structure of L² spaces.
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B.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
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C.
Bourgain–Tzafriri restricted invertibility principle
The Bourgain–Tzafriri restricted invertibility principle is a fundamental result in functional analysis and operator theory that guarantees the existence of large, well-invertible submatrices within certain classes of linear operators.
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D.
Banach–Stone theorem
The Banach–Stone theorem is a fundamental result in functional analysis that characterizes compact Hausdorff spaces via isometric isomorphisms between their spaces of continuous real- or complex-valued functions.
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E.
Gagliardo–Nirenberg interpolation inequalities
The Gagliardo–Nirenberg interpolation inequalities are fundamental results in functional analysis and partial differential equations that bound intermediate norms of functions by combinations of lower and higher order norms, playing a key role in regularity theory and nonlinear analysis.
- 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: Riesz–Thorin interpolation theorem Target entity description: The Riesz–Thorin interpolation theorem is a fundamental result in functional analysis that provides bounds for linear operators between Lᵖ spaces by interpolating their behavior between two known endpoint estimates.
-
A.
Riesz–Fischer theorem
The Riesz–Fischer theorem is a fundamental result in functional analysis that establishes the equivalence between square-summable sequences and square-integrable functions, providing the foundation for the Hilbert space structure of L² spaces.
-
B.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
-
C.
Bourgain–Tzafriri restricted invertibility principle
The Bourgain–Tzafriri restricted invertibility principle is a fundamental result in functional analysis and operator theory that guarantees the existence of large, well-invertible submatrices within certain classes of linear operators.
-
D.
Banach–Stone theorem
The Banach–Stone theorem is a fundamental result in functional analysis that characterizes compact Hausdorff spaces via isometric isomorphisms between their spaces of continuous real- or complex-valued functions.
-
E.
Gagliardo–Nirenberg interpolation inequalities
The Gagliardo–Nirenberg interpolation inequalities are fundamental results in functional analysis and partial differential equations that bound intermediate norms of functions by combinations of lower and higher order norms, playing a key role in regularity theory and nonlinear analysis.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
interpolation theorem
ⓘ
mathematical theorem ⓘ |
| appearsIn |
graduate textbooks on functional analysis
ⓘ
graduate textbooks on harmonic analysis ⓘ |
| applicableWhen | operator is linear ⓘ |
| appliesTo | linear operators between Lp and Lq spaces ⓘ |
| assumes | operator is bounded on two endpoint Lp spaces ⓘ |
| characteristic | interpolates exponents linearly in 1/p and 1/q ⓘ |
| concerns |
Lp spaces
ⓘ
bounded linear operators ⓘ complex interpolation ⓘ norm estimates ⓘ |
| consequence | convexity of log of operator norm in interpolation parameter ⓘ |
| contrastWith | real interpolation methods ⓘ |
| field |
functional analysis
ⓘ
harmonic analysis ⓘ operator theory ⓘ |
| generalizes | Riesz convexity theorem NERFINISHED ⓘ |
| gives | bounds for operator norms between Lp spaces ⓘ |
| hasVersion |
finite measure space version
ⓘ
sigma-finite measure space version ⓘ |
| historicalNote | proved independently by Marcel Riesz and Gunnar Thorin ⓘ |
| implies |
Lp boundedness from Lp0 and Lp1 bounds
ⓘ
intermediate operator norm estimate is log-convex in 1/p and 1/q ⓘ operator is bounded on intermediate Lp spaces ⓘ |
| influenced | development of modern interpolation theory ⓘ |
| involves |
holomorphic families of operators
ⓘ
strip in the complex plane ⓘ |
| isPartOf | interpolation theory of operators ⓘ |
| namedAfter |
Gunnar Thorin
NERFINISHED
ⓘ
Marcel Riesz NERFINISHED ⓘ |
| notApplicableTo | nonlinear operators in its standard form ⓘ |
| relatedConcept |
Banach space interpolation
NERFINISHED
ⓘ
Lp interpolation scale ⓘ |
| relatedTo |
Marcinkiewicz interpolation theorem
NERFINISHED
ⓘ
Stein interpolation theorem NERFINISHED ⓘ |
| requires | measure spaces to be sigma-finite in standard formulations ⓘ |
| typeOf | complex method interpolation result ⓘ |
| typicalAssumption | operator acts on simple functions and extends by density ⓘ |
| usedIn |
Fourier analysis
NERFINISHED
ⓘ
Lp-boundedness of Fourier transform related operators ⓘ ergodic theory ⓘ estimates for convolution operators ⓘ partial differential equations ⓘ probability theory ⓘ study of singular integral operators ⓘ |
| uses |
Hadamard three-lines theorem
NERFINISHED
ⓘ
complex analytic methods ⓘ |
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: Riesz–Thorin interpolation theorem Description of subject: The Riesz–Thorin interpolation theorem is a fundamental result in functional analysis that provides bounds for linear operators between Lᵖ spaces by interpolating their behavior between two known endpoint estimates.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.