On Centered and Weakly Centered Operators

We show that if C is a contraction of spectral radius 1 then T is polynomially bounded if and only if the same is true of T ⊗ C. As a corollary, we obtain that every invertible, centered, polynomially bounded operator is similar to a contraction. We also prove a structure theorem for weakly centered operators that satisfy a hypothesis of a technical nature.