On nth roots of bounded and unbounded quasinormal operators

Author:

Pietrzycki Paweł,Stochel Jan

Abstract

AbstractIn a recent paper (JFA 278:108342, 2020), R. E. Curto, S. H. Lee and J. Yoon asked the following question: LetTbe a subnormal operator, and assume that$$T^2$$ T 2 is quasinormal. Does it follow thatTis quasinormal? In (JFA 280:109001, 2021) we answered this question in the affirmative. In the present paper, we will extend this result in two directions. Namely, we prove that hyponormal (or even much beyond this class) nth roots of bounded quasinormal operators are quasinormal. On the other hand, we show that subnormal nth roots of unbounded quasinormal operators are quasinormal. We also prove that a non-normal quasinormal operator having a quasinormal nth root has a non-quasinormal nth root.

Funder

Uniwersytet Jagielloński w Krakowie

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics

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