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
Reference61 articles.
1. Ando, T.: Operators with a norm condition. Acta Sci. Math. (Szeged) 33, 169–178 (1972)
2. Agler, J.: Hypercontractions and subnormality. J. Operat. Theory 13, 203–217 (1985)
3. Ash, R.B.: Probability and Measure Theory. Harcourt/Academic Press, Burlington (2000)
4. Berg, C., Christensen, J.P.R., Ressel, P.: Harmonic Analysis on Semigroups. Springer-Verlag, Berlin (1984)
5. Birman, MSh., Solomjak, M.Z.: Spectral Theory of Selfadjoint Operators in Hilbert Space. D. Reidel Publishing Co., Dordrecht (1987)
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