What was already known
DFJP gave reflexive factorization and a basis when Y had a shrinking basis. Other positive cases covered certain special range spaces; arbitrary separable Y cannot qualify without an approximation property.
AI involvement
The model generated the proof search and essentially correct argument for the authors’ chosen problem. Antonio and Pablo Acuaviva checked references, corrected minor issues and edited the proof.
The paper says the Part II proof search was fully model-driven and humans supplied no next lemma or intermediate mathematics; later human verification and editing do not erase that proof-generation autonomy.
Importance
Extends basis factorization to the natural separable bounded-approximation-property range.
Limitations
The assertion requires a separable range with the bounded approximation property. Antonio and Pablo Acuaviva report checking the complete ordinary proof; no proof-assistant formalization is claimed.
Technical verification
Both authors report checking the complete printed ordinary proof by mathematical reading; no proof-assistant formalization is claimed.
Formal checking
Human mathematical reading, hypothesis and reference checks, correction and rewriting of the model proof
- Checker
- Antonio and Pablo Acuaviva
- Scope
- Problem 4 factorization theorem for weakly compact T into separable BAP range
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain the finite-rank approximation, DFJP interpolation, finite-dimensional decomposition, and basisification route.
Correction and publication history
Extends basis factorization to the natural separable bounded-approximation-property range.
Read this published revision