Theory of Linear Operations
E421064
Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Theory of Linear Operations canonical | 1 |
| Théorie des opérations linéaires | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4219668 — 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: Theory of Linear Operations Context triple: [Stefan Banach, notableWork, Theory of Linear Operations]
-
A.
Hilbert–Schmidt operators
Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
-
B.
Produits tensoriels topologiques et espaces nucléaires
"Produits tensoriels topologiques et espaces nucléaires" is a foundational 1953 doctoral thesis in functional analysis that introduced and developed the theory of nuclear spaces and topological tensor products.
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C.
Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
-
D.
Lectures on Cauchy’s problem in linear partial differential equations
"Lectures on Cauchy’s Problem in Linear Partial Differential Equations" is a classic mathematical treatise by Jacques Hadamard that systematically develops the theory of existence, uniqueness, and well-posedness for solutions to linear partial differential equations.
-
E.
Generalized Functions (multi-volume series)
Generalized Functions (multi-volume series) is a foundational multi-volume work in functional analysis and distribution theory that systematically develops the theory of generalized functions and its applications to differential equations and mathematical physics.
- 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: Theory of Linear Operations Target entity description: Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
-
A.
Hilbert–Schmidt operators
Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
-
B.
Produits tensoriels topologiques et espaces nucléaires
"Produits tensoriels topologiques et espaces nucléaires" is a foundational 1953 doctoral thesis in functional analysis that introduced and developed the theory of nuclear spaces and topological tensor products.
-
C.
Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
-
D.
Lectures on Cauchy’s problem in linear partial differential equations
"Lectures on Cauchy’s Problem in Linear Partial Differential Equations" is a classic mathematical treatise by Jacques Hadamard that systematically develops the theory of existence, uniqueness, and well-posedness for solutions to linear partial differential equations.
-
E.
Generalized Functions (multi-volume series)
Generalized Functions (multi-volume series) is a foundational multi-volume work in functional analysis and distribution theory that systematically develops the theory of generalized functions and its applications to differential equations and mathematical physics.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
monograph ⓘ nonfiction book ⓘ |
| associatedWith | Lwów School of Mathematics ⓘ |
| author | Stefan Banach ⓘ |
| citedBy |
Dieudonné: History of Functional Analysis
ⓘ
linked to:
History of Functional Analysis
Riesz and Sz.-Nagy: Functional Analysis ⓘ |
| contributedTo |
formal definition of Banach space
ⓘ
standardization of functional analytic notation ⓘ |
| countryOfOrigin | Poland ⓘ |
| describedAs |
cornerstone of functional analysis
ⓘ
first systematic treatise on Banach spaces ⓘ |
| describedBySource | foundational work in functional analysis ⓘ |
| fieldOfWork | mathematics ⓘ |
| genre | mathematical monograph ⓘ |
| hasImpactOn |
applied functional analysis
ⓘ
modern analysis textbooks ⓘ theory of topological vector spaces ⓘ |
| hasPart |
axiomatic treatment of normed linear spaces
ⓘ
results on Banach–Steinhaus theorem ⓘ results on Hahn–Banach theorem ⓘ results on closed graph theorem ⓘ results on open mapping theorem ⓘ spectral considerations for linear operators ⓘ study of dual spaces ⓘ study of series and sequences in Banach spaces ⓘ study of spaces of continuous functions ⓘ systematic study of bounded linear operators ⓘ |
| hasSubjectArea |
linear functional analysis
ⓘ
metric properties of function spaces ⓘ normed linear spaces ⓘ |
| inception | 1932 ⓘ |
| influenced |
development of modern functional analysis
ⓘ
operator theory ⓘ study of normed vector spaces ⓘ |
| languageOfWorkOrName | French ⓘ |
| mainSubject |
Banach spaces
ⓘ
functional analysis ⓘ linear operators ⓘ |
| originalTitle |
Théorie des opérations linéaires
ⓘ
linked to:
Theory of Linear Operations
|
| partOf | early 20th-century foundations of functional analysis ⓘ |
| placeOfPublication | Warsaw ⓘ |
| publicationDate | 1932 ⓘ |
| publicationSeries | Monografie Matematyczne (Mathematical Monographs) ⓘ |
| publisher | Monografje Matematyczne ⓘ |
| timePeriod | interwar period ⓘ |
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: Theory of Linear Operations Description of subject: Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Theory of Linear Operations