From the 2 of 16 linked papers with an AI index.
16 papers
Banach's Isometric Conjecture over the Complex Field
Antonio Acuaviva, Tomasz Kania
We complete Banach's isometric conjecture over the complex field. More precisely, if \(X\) is a complex normed space and, for some \(2\leqslant n<\dim_{\C}X\), all its \(n\)-dimens…
CNOT-Distance is NP-complete under all-to-all connectivity
Antonio Acuaviva, Arturo Acuaviva, Pablo Acuaviva
Given and an integer , we ask whether can be implemented by at most CNOT gates on fixed labelled wires with all-to-all connectivity. We prov…
Mathematical Discovery in the Wild: AI-Guided Proofs in Banach Space Theory
Antonio Acuaviva, Pablo Acuaviva
We investigate the capacity of current language models to contribute to mathematical research. In Banach space theory, AI systems generated key ideas and proofs for five new result…
A Unital Banach Algebra Which Is Not a Calkin Algebra
Antonio Acuaviva, Pablo Acuaviva
The authors construct a unital Banach algebra of continuum density with exactly one non‑zero proper closed two‑sided ideal and prove that it cannot be isomorphic to any Calkin alge…
A Separable Banach Space with a Schauder Basis Which Is Not a Lipschitz Retract of Its Bidual
Antonio Acuaviva
The paper constructs a separable Banach space with a Schauder basis whose unit ball is not a uniformly continuous (and thus not Lipschitz) retract of its bidual’s unit ball, showin…
Pure infiniteness and primary factorisation
Antonio Acuaviva, Bence Horváth, Tomasz Kania
We show that there is no real or complex indecomposable Banach space with the primary factorisation property (PFP). We relate the PFP of a Banach space to ring-theoretic infini…