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Record W2575853203 · doi:10.1515/crelle-2017-0056

A new proof of the Tikuisis–White–Winter theorem

2018· preprint· en· W2575853203 on OpenAlex
Christopher Schafhauser

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) · 2018
Typepreprint
Languageen
FieldMathematics
TopicAdvanced Operator Algebra Research
Canadian institutionsUniversity of Waterloo
Fundersnot available
KeywordsMathematicsMultiplicative functionSeparable spaceTRACE (psycholinguistics)Centralizer and normalizerTrace classVon Neumann architecturePure mathematicsNorm (philosophy)Operator algebraVon Neumann algebraAffiliated operatorDiscrete mathematicsAlgebra over a fieldJordan algebraHilbert spaceAlgebra representationMathematical analysis

Abstract

fetched live from OpenAlex

Abstract A trace on a <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup><m:mi mathvariant="normal">C</m:mi><m:mo>*</m:mo></m:msup></m:math> {\mathrm{C}^{*}} -algebra is amenable (resp. quasidiagonal) if it admits a net of completely positive, contractive maps into matrix algebras which approximately preserve the trace and are approximately multiplicative in the 2-norm (resp. operator norm). Using that the double commutant of a nuclear <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup><m:mi mathvariant="normal">C</m:mi><m:mo>*</m:mo></m:msup></m:math> {\mathrm{C}^{*}} -algebra is hyperfinite, it is easy to see that traces on nuclear <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup><m:mi mathvariant="normal">C</m:mi><m:mo>*</m:mo></m:msup></m:math> {\mathrm{C}^{*}} -algebras are amenable. A recent result of Tikuisis, White, and Winter shows that faithful traces on separable, nuclear <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup><m:mi mathvariant="normal">C</m:mi><m:mo>*</m:mo></m:msup></m:math> {\mathrm{C}^{*}} -algebras in the UCT class are quasidiagonal. We give a new proof of this result using the extension theory of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup><m:mi mathvariant="normal">C</m:mi><m:mo>*</m:mo></m:msup></m:math> {\mathrm{C}^{*}} -algebras and, in particular, using a version of the Weyl–von Neumann Theorem due to Elliott and Kucerovsky.

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)0.004
metaresearch head score (Gemma)0.003
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Research integrity, Insufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.853
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0040.003
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0020.002
Bibliometrics0.0010.001
Science and technology studies0.0010.001
Scholarly communication0.0010.000
Open science0.0040.003
Research integrity0.0010.006
Insufficient payload (model declined to judge)0.0020.000

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 head0.044
GPT teacher head0.364
Teacher spread0.320 · 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