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Record W1971587484 · doi:10.1112/s0024610704005423

ON THE NORM OF ELEMENTARY OPERATORS

2004· article· en· W1971587484 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueJournal of the London Mathematical Society · 2004
Typearticle
Languageen
FieldMathematics
TopicDifferential Equations and Boundary Problems
Canadian institutionsUniversité Laval
Fundersnot available
KeywordsMathematicsBounded functionHilbert spaceSubalgebraApproximation propertyNorm (philosophy)Linear operatorsPure mathematicsOperator normOperator theoryBanach spaceAlgebra over a fieldDiscrete mathematicsMathematical analysis

Abstract

fetched live from OpenAlex

The norm problem is considered for elementary operators of the form Ua,b: A→A,x↦ axb+bxa (a,b∈A) in the special case when A is a subalgebra of the algebra of bounded operators on a Banach space. In particular, the lower estimate ‖ ‖ U a , b ‖ ⩾ ‖ a ‖ ‖ b ‖ is established when the Banach space is a Hilbert space and A is the algebra of all bounded linear operators.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.009
Threshold uncertainty score0.445

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.035
GPT teacher head0.285
Teacher spread0.250 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it