Abstract. In [17], M. Uchiyama gave necessary and sufficient conditions for contractions to be quasiaffine transforms, quasisimilar, or similar to unilateral shifts of finite multiplicity in terms of norm-estimates of complete analytic families of eigenvectors of their adjoints. In this paper, the result for contractions to be quasiaffine transforms of unilateral shifts is generalized to power bounded operators. It is shown that the result for contractions to be quasisimilar or similar to unilateral shifts can't be extended to power bounded operators: a counterexample is given. No curvature of the holomorphic vector bundle generated by eigenvectors of operators is computed.

DOI: 10.14232/actasm-015-060-1

AMS Subject Classification (1991): 47A05, 47B99, 47B32, 30H10

Keyword(s): power bounded operator, unilateral shift, quasiaffine transform, quasisimilarity, contraction, analytic family of eigenvalues, similarity

Received August 11, 2015, and in revised form September 6, 2016. (Registered under 60/2015.)