Strict Cosingularity and Adjoints for Separable Range
Statement
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.
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No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
Antonio Acuaviva and Pablo Acuaviva, using ChatGPT 5.5 ProThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
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.
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