Bibliographic record
Abstract
Stability theory has caught the attention of mathematicians in many areas, such as model theory and functional analysis.In particular, in the early 80's, J.-L.Krivine and B. Maurey introduced the concept of stable Banach spaces.This stability has a significant impact on the geometry of such spaces.They proved that any separable infinite-dimensional stable Banach space contains a copy of l p for some p ∈ [1, ∞) almost isometrically.Recently, S. Ferri and M. Neufang introduced the notion of multiplicative stability of Banach algebras as an analogue of stability of Banach spaces in Krivine-Maurey's sense, to which they refer as additive stability.In this work, we investigate properties of multiplicative and additive stability of Banach algebras such as the l p -direct sum of a sequence of multiplicatively stable Banach algebras, and the relation between additive stability and Arens regularity in a certain class of Banach algebras.Further, we introduce hyper-instability as a strong version of multiplicative instability.Moreover, we study multiplicative stability of some well-known Banach algebras.We define and study a stronger and a weaker version of multiplicative stability, inspired by spaces of functions on topological semigroups, namely, almost periodic and tame functions.Based on our work, we introduce a dynamical hierarchy of Banach algebras, which is a new classification of Banach algebras.This classification puts dividing lines to measure, in a sense, multiplicative stability of Banach algebras.
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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 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 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 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".