Strong and Extremely Strong Ditkin sets for the Banach Algebras<i>A<sub>p</sub><sup>r</sup></i>(<i>G</i>) =<i>A</i><sub><i>p</i></sub>⋂<i>L</i><sup><i>r</i></sup>(<i>G</i>)
Bibliographic record
Abstract
Abstract Let A p ( G ) be the Figa-Talamanca, Herz Banach Algebra on G ; thus A 2 ( G ) is the Fourier algebra. Strong Ditkin (SD) and Extremely Strong Ditkin (ESD) sets for the Banach algebras A p r ( G ) are investigated for abelian and nonabelian locally compact groups G . It is shown that SD and ESD sets for A p ( G ) remain SD and ESD sets for A p r ( G ), with strict inclusion for ESD sets. The case for the strict inclusion of SD sets is left open. A result on the weak sequential completeness of A 2 ( F ) for ESD sets F is proved and used to show that Varopoulos, Helson, and Sidon sets are not ESD sets for A 2 r ( G ), yet they are such for A 2 ( G ) for discrete groups G , for any 1 ≤ r ≤ 2. A result is given on the equivalence of the sequential and the net definitions of SD or ESD sets for σ -compact groups. The above results are new even if G is abelian.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; both teacher heads agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".