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arXiv · 2103.09961

On $n$th roots of bounded and unbounded quasinormal operators

Paweł Pietrzycki·Jan Stochel
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Abstract

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.

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Paweł Pietrzycki, Jan Stochel. 2021-03-18. On $n$th roots of bounded and unbounded quasinormal operators. https://doi.org/10.1007/s10231-022-01281-z

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