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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2103.09961 |
| Etiquetas: |
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- In a recent paper [9], R. E. Curto, S. H. Lee and J. Yoon asked the following question: Let $T$ be a subnormal operator, and assume that $T^2$ is quasinormal. Does it follow that $T$ is quasinormal?. In [36] we answered this question in the affirmative. In the present paper, we will extend this result in two directions. Namely, we prove that both class A $n$th roots of bounded quasinormal operators and subnormal $n$th roots of unbounded quasinormal operators are quasinormal. We also show that a non-normal quasinormal operator having a quasinormal $n$th root has a non-quasinormal $n$th root.