On $n$th roots of bounded and unbounded quasinormal operators

Abstract

In a recent paper [9], R. E. Curto, S. H. Lee and J. Yoon asked the following question: Let $T$ be a subnormal operator, and assume that $T^2$ is quasinormal. Does it follow that $T$ is quasinormal?. In [36] we answered this question in the affirmative. In the present paper, we will extend this result in two directions. Namely, we prove that both class A $n$th roots of bounded quasinormal operators and subnormal $n$th roots of unbounded quasinormal operators are quasinormal. We also show that a non-normal quasinormal operator having a quasinormal $n$th root has a non-quasinormal $n$th root.

References in corpus (2)

• Quasinormality of powers of commuting pairs of bounded operators
• Subnormal $n$th roots of quasinormal operators are quasinormal

Cited by in corpus (1)

• Unbounded operators having self-adjoint or normal powers and some related results