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

Subnormal $n$th roots of quasinormal operators are quasinormal