Bibliographic record
Abstract
We say that a C⁎-algebra is soft if it has no nonzero unital quotients, and we connect this property to the Hjelmborg-Rørdam condition for stability and to property (S) of Ortega-Perera-Rørdam. We further say that an operator in a C⁎-algebra is soft if its associated hereditary subalgebra is, and we provide useful spectral characterizations of this concept. Of particular interest are C⁎-algebras that have an abundance of soft elements in the sense that every hereditary subalgebra contains an almost full soft element. We show that this property is implied by the Global Glimm Property, and that every C⁎-algebra with an abundance of soft elements is nowhere scattered. This sheds new light on the long-standing Global Glimm Problem of whether every nowhere scattered C⁎-algebra has the Global Glimm Property.
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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 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| 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".