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On Similarity to Normal Operators

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Abstract

This paper gives a characterization of the asymptotic limit A T associated to a contraction T that is similar to a normal operator (Theorem 2). Extensions from contractions to power bounded operators intertwined to a contraction with a \({\mathcal{C}_{0}}\). completely nonunitary part (not necessarily a normaloid contraction) are considered as well (Theorem 1). It is also given a characterization of the asymptotic limit A T for a hyponormal contraction T, and it is shown that if a hyponormal contraction has no nontrivial invariant subspace, then one of the defect operators is not finite-rank (Corollary 1).

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  1. Catholic University of Rio de Janeiro, Rio de Janeiro, RJ, 22453-900, Brazil

    Carlos S. Kubrusly

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  1. Carlos S. Kubrusly
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Kubrusly, C.S. On Similarity to Normal Operators. Mediterr. J. Math. 13, 2073–2085 (2016). https://doi.org/10.1007/s00009-015-0622-3

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