What was already known
Hu and Ji proved the full interval under narrower reciprocal-weight conditions. Ji and Zhang also asked whether 1 belongs to Λ(T) for every quasinilpotent operator.
AI involvement
Ignatev credits Claude Opus with decisively formulating and proving the max-term lemma. Ignatev directed, revised and verified the output and supplied the application.
The author singles out Claude’s decisive Lemma 1, used twice in the weighted-shift theorem, but does not credit the model with the broader Theorem 3.
Importance
Extends the weighted-shift class for which the full power set is known.
Limitations
The paper’s general Banach-space answer to Ji and Zhang is a separate human-attributed Baire-category argument. The model-origin contribution assessed here is the lemma and its use in the weighted-shift theorem; no independent check was located.
Technical verification
Ignatev reports revising and verifying all generated output, including Lemma 1 and its use. This is a source-reported author check, not a reproduced check.
Independent checking
Revision and verification of Claude output
- Checker
- Egor Ignatev, paper author
- Scope
- Lemma 1 max-term asymptotic supporting Theorem 4 for decreasing p′-summable shift weights
- Basis
- Reported by the linked checker
Human understanding
Ignatev revised the model lemma and explains how the convex weight function and max-term estimate control the numerator and denominator of the resolvent exponent.
Correction and publication history
Extends the weighted-shift class for which the full power set is known.
Read this published revision