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 LetAp(G) be the Figa-Talamanca, Herz Banach Algebra onG; thusA2(G) is the Fourier algebra. Strong Ditkin (SD) and Extremely Strong Ditkin (ESD) sets for the Banach algebrasApr(G) are investigated for abelian and nonabelian locally compact groupsG. It is shown that SD and ESD sets forAp(G) remain SD and ESD sets forApr(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 ofA2(F) for ESD setsFis proved and used to show that Varopoulos, Helson, and Sidon sets are not ESD sets forA2r(G), yet they are such forA2(G) for discrete groupsG, for any 1 ≤r≤ 2. A result is given on the equivalence of the sequential and the net definitions of SD or ESD sets forσ-compact groups. The above results are new even ifGis abelian.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
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".