Power boundedness and similarity to contractions for some perturbations of isometries

The relation between power boundedness and similarity to a contraction has been thoroughly investigated by Cassier (1999) for a certain class of operators on Hilbert space. We explore the application of those results to one-dimensional perturbations of the shift operator. The criteria obtained lead to various connections with function theory problems.  2004 Elsevier Inc. All rights reserved.