Posinormality and the Root Problem
Functional Analysis
2026-01-13 v1
Abstract
The paper extends three results regarding the nth root problem by embedding classes of Hilbert-space operators into the class of posinormal operators. For instance, it is shown that (i) for coposinormal operators, if T is paranormal and T^n is quasinormal, then T is normal, and (ii) for posinormal operators, if T is k-quasiparanormal and T^n is normal, then T is normal. Moreover, (iii) it is also shown that the latter result is not conditioned to the separability of the underlying Hilbert space, even if T is not posinormal, where, in such a case, T is the direct sum of a normal operator with a nilpotent one.
Cite
@article{arxiv.2601.07203,
title = {Posinormality and the Root Problem},
author = {C. S. Kubrusly and H. M Stankovic},
journal= {arXiv preprint arXiv:2601.07203},
year = {2026}
}