On $n$th roots of bounded and unbounded quasinormal operators
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866910920915025920 |
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| author | Pietrzycki, Paweł Stochel, Jan |
| author_facet | Pietrzycki, Paweł Stochel, Jan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_09961 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On $n$th roots of bounded and unbounded quasinormal operators Pietrzycki, Paweł Stochel, Jan Functional Analysis 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. |
| title | On $n$th roots of bounded and unbounded quasinormal operators |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2103.09961 |