Subnormal $n$th roots of quasinormal operators are quasinormal

Abstract

In the recent paper, 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 $n$th roots of quasinormal operators are quasinormal.

References in corpus (1)

• Quasinormality of powers of commuting pairs of bounded operators

Cited by in corpus (3)

• On $n$th roots of bounded and unbounded quasinormal operators
• Two-moment characterization of spectral measures on the real line
• Unbounded operators having self-adjoint or normal powers and some related results