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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 rests unknown.
AMS Subject Classification
(1991): 47A05, 47B99, 47B15
Keyword(s):
power bounded operator,
singular unitary operator,
similarity,
quasisimilarity,
quasiaffine transform
Received April 8, 2010, and in revised form October 12, 2010. (Registered under 24/2010.)
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