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Amenable operators on Hilbert spaces

2005· article· de· W2080266767 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 für die reine und angewandte Mathematik (Crelles Journal) · 2005
Typearticle
Languagede
FieldMathematics
TopicAdvanced Operator Algebra Research
Canadian institutionsUniversity of WaterlooUniversity of Regina
Fundersnot available
KeywordsSubalgebraComplement (music)Spectrum (functional analysis)MathematicsOperator (biology)Hilbert spacePure mathematicsAlgebra over a fieldOperator algebraDiscrete mathematicsPhysicsQuantum mechanicsComplementation

Abstract

fetched live from OpenAlex

In this paper, we study the closed subalgebra AT of ℬ(ℋ) generated by an operator T. We show that AT is amenable if and only if T is similar to a normal operator whose spectrum has connected complement and no interior. Furthermore, if AT is amenable, then AT is similar to a C*-algebra. We also prove that if T has finite spectrum, then AT is weakly amenable if and only if AT is amenable. In particular, if Q ∈ ℬ(ℋ) is quasinilpotent, then AQ is weakly amenable if and only if Q = 0.

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)0.005
metaresearch head score (Gemma)0.003
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Science and technology studies, Scholarly communication, Research integrity, Insufficient payload (model declined to judge)
Consensus categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: Not applicable
GenreCandidate signal: Review · Consensus signal: none
Teacher disagreement score0.250
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0050.003
Meta-epidemiology (narrow)0.0020.001
Meta-epidemiology (broad)0.0030.002
Bibliometrics0.0020.001
Science and technology studies0.0030.000
Scholarly communication0.0050.002
Open science0.0020.001
Research integrity0.0010.007
Insufficient payload (model declined to judge)0.0050.005

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 head0.033
GPT teacher head0.349
Teacher spread0.316 · 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