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arXiv · 2008.04758

Subnormal $n$th roots of quasinormal operators are quasinormal

Paweł Pietrzycki·Jan Stochel
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Abstract

In the recent paper, R. E. Curto, S. H. Lee, J. Yoon, asked the following question: Let $A$ be a subnormal operator, and assume that $A^2$ is quasinormal. Does it follow that $A$ is quasinormal? In this paper, we give an affirmative answer to this question. In fact, we prove more general result that subnormal $n$th roots of quasinormal operators are quasinormal.

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BibTeXRIS

Paweł Pietrzycki, Jan Stochel. 2020-08-08. Subnormal $n$th roots of quasinormal operators are quasinormal. https://doi.org/10.1016/j.jfa.2021.109001

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