Quasiaffine transforms of polynomially bounded operators (Q1293308)

The main result of this article is a theorem stating that every polynomially bounded operator is a quasiaffine transform of a contraction. The proof is based on Bourgain's theorem on the disc algebra. Moreover, the set of contractions of class \(C_0\) is extended to include polynomially bounded operators which are not necessarily of norm \(\leq 1\). It is shown that every operator in this extended class is polynomially bounded, so the above result applies in particular to such operators. The authors prove that if \(T\) is of class \(C_0\) the assertion can be strengthened in the sense that there is a quasiaffine transform \(T_1\) of \(T\) which is of class \(C_0\) such that \(T\) and \(T_1\) are quasisimilar.