Similarity results for operators of class C0
Abstract
If T is a multiplicity-free contraction of class C0 with minimal function mT, then it is quasisimilar to the Jordan block S(mT). In case mT is a Blaschke product with simple roots forming a Carleson sequence, we show that the relation between T and S(mT) can be strengthened to similarity. Under the additional assumption that u(T) has closed range for every inner divisor u of mT, the result also holds in the more general setting where the roots have bounded multiplicities.
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