What was already known
Earlier negative examples excluded realization as a Calkin algebra only for separable X, leaving nonseparable spaces open.
AI involvement
The model generated essentially correct arguments for the two constructions in a human-chosen problem. Kania proposed the question; Antonio and Pablo Acuaviva checked and explained the retained proofs.
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
Answers the general unital Banach-algebra realization question across Banach spaces of any density.
Limitations
The result concerns complex unital Banach-algebra isomorphism, not a classification of Calkin algebras. The authors report checking both final constructions as ordinary proofs.
Technical verification
The authors report checking both final constructions as ordinary mathematical proofs; no machine formalization is claimed.
Formal checking
Human mathematical proof and citation checking, minor corrections and rewriting
- Checker
- Antonio and Pablo Acuaviva
- Scope
- Theorem 6.1, a unital complex Banach algebra not Calkin over any X
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain large-density/topological-simplicity construction and the noncompact separable-range contradiction.
Correction and publication history
Answers the general unital Banach-algebra realization question across Banach spaces of any density.
Read this published revision