Abstract
If T is a multiplicity-free contraction of class C 0 with minimal function m T , then it is quasisimilar to the Jordan block S(m T ). In case m T is a Blaschke product with simple roots forming a Carleson sequence, we show that the relation between T and S(m T ) can be strengthened to similarity. Under the additional assumption that u(T) has closed range for every inner divisor \({u\in H^\infty}\) of m T , the result also holds in the more general setting where the roots have bounded multiplicities.
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Research supported by NSERC (Canada).
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Clouâtre, R. Similarity Results for Operators of Class C 0 . Integr. Equ. Oper. Theory 71, 557–573 (2011). https://doi.org/10.1007/s00020-011-1916-x
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DOI: https://doi.org/10.1007/s00020-011-1916-x