English

Subnormal $n$th roots of quasinormal operators are quasinormal

Functional Analysis 2025-04-30 v3

Abstract

In the recent paper, R. E. Curto, S. H. Lee, J. Yoon, asked the following question: Let AA be a subnormal operator, and assume that A2A^2 is quasinormal. Does it follow that AA is quasinormal? In this paper, we give an affirmative answer to this question. In fact, we prove more general result that subnormal nnth roots of quasinormal operators are quasinormal.

Keywords

Cite

@article{arxiv.2008.04758,
  title  = {Subnormal $n$th roots of quasinormal operators are quasinormal},
  author = {Paweł Pietrzycki and Jan Stochel},
  journal= {arXiv preprint arXiv:2008.04758},
  year   = {2025}
}