Artin approximation over Banach spaces
arXiv:2004.08877
Abstract
We give examples showing that the usual Artin Approximation theorems valid for convergent series over a field are no longer true for convergent series over a commutative Banach algebra. In particular we construct an example of a commutative integral Banach algebra such that the ring of formal power series over is not flat over the ring of convergent power series over .
To appear in Commun. Algebra