On Similarity to Normal Operators

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• 作者：Carlos S. Kubrusly
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：13
• 期：4
• 页码：2073-2085
• 全文大小：536 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454
• 卷排序：13

文摘

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).Mathematics Subject ClassificationPrimary 47A1547A45Secondary 47B1547B20