A Hilbert Space Problem Book
E1041774
A Hilbert Space Problem Book is a classic problem-oriented textbook by Paul Halmos that presents and explores key concepts in Hilbert space theory through a comprehensive collection of exercises and solutions.
All labels observed (1)
| Label | Occurrences |
|---|---|
| A Hilbert Space Problem Book canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T13444244 — 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: A Hilbert Space Problem Book Context triple: [Paul Halmos, notableWork, A Hilbert Space Problem Book]
-
A.
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.
-
B.
Leçons d’analyse fonctionnelle
Leçons d’analyse fonctionnelle is a foundational textbook in functional analysis that helped shape the modern theory of linear operators and Banach and Hilbert spaces.
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C.
Hilbert spaces
Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
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D.
Foundations of Modern Analysis
Foundations of Modern Analysis is a classic graduate-level textbook that systematically develops modern mathematical analysis using rigorous, abstract methods and functional analysis.
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E.
Functional Analysis: Introduction to Further Topics in Analysis
"Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential 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: A Hilbert Space Problem Book Target entity description: A Hilbert Space Problem Book is a classic problem-oriented textbook by Paul Halmos that presents and explores key concepts in Hilbert space theory through a comprehensive collection of exercises and solutions.
-
A.
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.
-
B.
Leçons d’analyse fonctionnelle
Leçons d’analyse fonctionnelle is a foundational textbook in functional analysis that helped shape the modern theory of linear operators and Banach and Hilbert spaces.
-
C.
Hilbert spaces
Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
-
D.
Foundations of Modern Analysis
Foundations of Modern Analysis is a classic graduate-level textbook that systematically develops modern mathematical analysis using rigorous, abstract methods and functional analysis.
-
E.
Functional Analysis: Introduction to Further Topics in Analysis
"Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematics textbook ⓘ problem book ⓘ |
| author |
Paul Halmos
NERFINISHED
ⓘ
Paul R. Halmos NERFINISHED ⓘ |
| contains |
hints
ⓘ
problems ⓘ solutions ⓘ |
| emphasizes |
applications of Hilbert space theory
ⓘ
problem solving in functional analysis ⓘ |
| field |
Hilbert space theory
ⓘ
functional analysis ⓘ |
| focus | rigorous treatment of Hilbert space concepts ⓘ |
| genre |
academic textbook
ⓘ
mathematics ⓘ |
| hasReputation |
classic text in Hilbert space theory
ⓘ
standard reference in functional analysis education ⓘ |
| intendedAudience |
advanced undergraduates in mathematics
ⓘ
graduate students in mathematics ⓘ researchers in functional analysis ⓘ |
| language | English ⓘ |
| notableFor |
comprehensive collection of Hilbert space exercises
ⓘ
detailed solutions to problems ⓘ systematic development of Hilbert space theory via problems ⓘ |
| pedagogicalApproach |
exercise-based
ⓘ
problem-oriented ⓘ |
| structure | chapters organized by topic in Hilbert space theory ⓘ |
| subject |
Banach spaces related to Hilbert spaces
ⓘ
Fourier series in Hilbert space ⓘ Hilbert spaces ⓘ bounded linear operators ⓘ compact operators ⓘ invariant subspaces ⓘ normal operators ⓘ operator theory ⓘ orthonormal bases ⓘ projections on Hilbert space ⓘ self-adjoint operators ⓘ spectral measures ⓘ spectral theory ⓘ unbounded operators ⓘ |
| usedAs |
course text in functional analysis
ⓘ
reference for Hilbert space theory ⓘ |
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: A Hilbert Space Problem Book Description of subject: A Hilbert Space Problem Book is a classic problem-oriented textbook by Paul Halmos that presents and explores key concepts in Hilbert space theory through a comprehensive collection of exercises and solutions.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.