Subnormal $n$th roots of quasinormal operators are quasinormal

Abstract

In the recent paper [7], 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-roots of quasinormal operators are quasinormal.