Introduction to Hilbert Space and the Theory of Spectral Multiplicity
E1041773
"Introduction to Hilbert Space and the Theory of Spectral Multiplicity" is a classic mathematical text by Paul Halmos that provides a foundational treatment of Hilbert space theory and the spectral analysis of linear operators.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Introduction to Hilbert Space and the Theory of Spectral Multiplicity canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T13444243 — 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: Introduction to Hilbert Space and the Theory of Spectral Multiplicity Context triple: [Paul Halmos, notableWork, Introduction to Hilbert Space and the Theory of Spectral Multiplicity]
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A.
Les algèbres d’opérateurs dans l’espace hilbertien
Les algèbres d’opérateurs dans l’espace hilbertien is a foundational monograph by Jacques Dixmier that systematically develops the theory of operator algebras on Hilbert spaces, particularly C*-algebras and von Neumann algebras.
-
B.
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.
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C.
Introduction to Abstract Harmonic Analysis
Introduction to Abstract Harmonic Analysis is a foundational graduate-level textbook that systematically develops the theory of harmonic analysis on topological groups and related abstract structures.
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D.
Theory of Linear Operations
Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
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E.
Harmonic Analysis and the Theory of Probability
Harmonic Analysis and the Theory of Probability is a seminal mathematical monograph that connects Fourier-analytic methods with probabilistic concepts, helping to lay the foundations of modern probability theory.
- 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: Introduction to Hilbert Space and the Theory of Spectral Multiplicity Target entity description: "Introduction to Hilbert Space and the Theory of Spectral Multiplicity" is a classic mathematical text by Paul Halmos that provides a foundational treatment of Hilbert space theory and the spectral analysis of linear operators.
-
A.
Les algèbres d’opérateurs dans l’espace hilbertien
Les algèbres d’opérateurs dans l’espace hilbertien is a foundational monograph by Jacques Dixmier that systematically develops the theory of operator algebras on Hilbert spaces, particularly C*-algebras and von Neumann algebras.
-
B.
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.
-
C.
Introduction to Abstract Harmonic Analysis
Introduction to Abstract Harmonic Analysis is a foundational graduate-level textbook that systematically develops the theory of harmonic analysis on topological groups and related abstract structures.
-
D.
Theory of Linear Operations
Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
-
E.
Harmonic Analysis and the Theory of Probability
Harmonic Analysis and the Theory of Probability is a seminal mathematical monograph that connects Fourier-analytic methods with probabilistic concepts, helping to lay the foundations of modern probability theory.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
monograph ⓘ nonfiction book ⓘ |
| associatedWith |
20th-century mathematics
ⓘ
American mathematical literature ⓘ |
| author |
Paul Halmos
ⓘ
Paul R. Halmos ⓘ
linked to:
Paul Halmos
|
| coversTopic |
bounded linear operators
ⓘ
inner product spaces ⓘ measure-theoretic methods in operator theory ⓘ multiplicity theory of spectra ⓘ orthonormal bases ⓘ self-adjoint operators ⓘ spectral measures ⓘ spectral theorem ⓘ unitary operators ⓘ |
| describedAs |
classic text in Hilbert space theory
ⓘ
foundational treatment of Hilbert space and spectral multiplicity ⓘ |
| field |
functional analysis
ⓘ
mathematics ⓘ operator theory ⓘ |
| genre |
graduate-level textbook
ⓘ
textbook ⓘ |
| hasConcept |
cyclic subspaces
ⓘ
direct integral decomposition ⓘ multiplicity function of a spectral measure ⓘ normal operators ⓘ orthogonal decomposition of Hilbert spaces ⓘ projection-valued measures ⓘ spectral types ⓘ |
| hasInfluenceOn |
modern treatments of Hilbert space theory
ⓘ
subsequent textbooks on operator theory ⓘ |
| intendedAudience |
advanced undergraduates in mathematics
ⓘ
graduate students in mathematics ⓘ researchers in functional analysis ⓘ |
| language | English ⓘ |
| mainSubject |
Hilbert space
ⓘ
linear operators on Hilbert space ⓘ spectral multiplicity ⓘ spectral theory ⓘ |
| relatedWork |
A Hilbert Space Problem Book by Paul R. Halmos
ⓘ
linked to:
A Hilbert Space Problem Book
Measure Theory by Paul R. Halmos ⓘ |
| usedAs |
reference in functional analysis
ⓘ
textbook for courses on Hilbert spaces ⓘ |
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: Introduction to Hilbert Space and the Theory of Spectral Multiplicity Description of subject: "Introduction to Hilbert Space and the Theory of Spectral Multiplicity" is a classic mathematical text by Paul Halmos that provides a foundational treatment of Hilbert space theory and the spectral analysis of linear operators.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject linked to:
Halmos