Strict Cosingularity and Adjoints for Separable Range
Pełczyński's duality between strictly singular and strictly cosingular operators fails without weak compactness. Beanland asked, in work with Androulakis and later on MathOverflow, for the separable-range case: the paper answers it affirmatively and shows that for separable , is strictly cosingular exactly when is strictly singular.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Banach Space Operator Ideals
- Posed by
- Kevin Beanland
- Year posed
- 2008
- Years open
- 18y
- Solved
- 2026-07-19
- Model
- ChatGPT 5.5 Pro
- Vendor
- OpenAI
- Collaborators
- Antonio Acuaviva, Pablo Acuaviva
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
ChatGPT 5.5 Pro, driven directly and through Codex agents over a filesystem, generated the key ideas and the proof; the authors verified and refined it. The paper reports that the model sometimes misattributed a theorem, cited a result imprecisely, or presented steps as immediate when they still needed checking, so the human verification was load-bearing. The authors state none of these results came from the newer generation of models.
Verification
No independent check. The proof stands on verification by the paper's authors, who describe correcting misattributions and filling in steps the model presented as immediate. Preprint, not refereed.
Sources
Submitted by Curator34