A counterexample on continuous coprime factors

Extension of the ν-metric

“…Note that the projective freeness of R, although it comes close, does not quite guarantee that the reverse containment in (2.5) holds, since we insist that every element in S(R, p, m) has a normalized right and left coprime factorization. Given a right and left coprime factorization, the existence of a normalized right and left coprime factorization is not automatic in general, as was pointed out by Sergei Treil [22], where he gave an explicit example where this fails when R is the disk algebra A(D).…”