Bibliographic record
Abstract
For a Banach space X X defined in terms of a big- O O condition and its subspace x defined by the corresponding little- o o condition, the biduality property (generalizing the concept of reflexivity) asserts that the bidual of x is naturally isometrically isomorphic to X X . The property is known for pairs of many classical function spaces (such as ( ℓ ∞ , c 0 ) (\ell _\infty , c_0) , (BMO, VMO), (Lip, lip), etc.) and plays an important role in the study of their geometric structure. The present paper is devoted to the biduality property for traces to closed subsets S ⊂ R n S\subset \mathbb {R}^n of a generalized Zygmund space Z ω ( R n ) Z^\omega (\mathbb {R}^n) . The method of the proof is based on a careful analysis of the structure of geometric preduals of the trace spaces along with a powerful finiteness theorem for the trace spaces Z ω ( R n ) | S Z^\omega (\mathbb {R}^n)|_S .
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.012 | 0.002 |
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".