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).
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.
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".