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Bibliographic record
Abstract
Weak amenability of a weighted group algebra, or a Beurling algebra, is a long-standing open problem.The commutative case has been extensively investigated and fully characterized.We study the non-commutative case.Given a weight function ω on a locally compact group G, we characterize derivations from L 1 (G, ω) into its dual in terms of certain functions.Then we show that for a locally compact IN group G, if there is a non-zero continuous group homomorphism ϕ: G → C such that ϕ(x)/ω(x)ω(x -1 ) is bounded on G, then L 1 (G, ω) is not weakly amenable.Some useful criteria that rule out weak amenability of L 1 (G, ω) are established.Using them we show that for many polynomial type weights the weighted Heisenberg group algebra is not weakly amenable, neither is the weighted ax + b group algebra.We further study weighted quotient group algebra L 1 (G/H, ω), where ω is the canonical weight on G/H induced by ω.We reveal that the kernel of the canonical homomorphism from L 1 (G, ω) to L 1 (G/H, ω) is complemented.This allows us to obtain some sufficient conditions under which L 1 (G/H, ω) inherits weak amenability of L 1 (G, ω).We study further weak amenability of Beurling algebras of subgroups.In general, weak amenability of a Beurling algebra does not pass to the Beurling algebra of a subgroup.However, in some circumstances this inheritance can happen.We also give an example to show that weak amenability of both L 1 (H, ω| H ) and L 1 (G/H, ω) does not ensure weak amenability of L 1 (G, ω).
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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 it