On power bounded operators that are quasiaffine tranforms of singular unitaries

Abstract

In [9] a question is raised: if a power bounded operator is quasisimilar to a singular unitary operator, is it similar to this unitary operator? For polynomially bounded operators, a positive answer to this question is known [1], [13]. In this paper a positive answer is given in some particular cases, but in general an answer remains unknown.

Acta Sci. Math. (Szeged), 77(2011), 589-606. A misprint in the formulation of Theorem 2.5 is corrected