Unbounded operators having self‐adjoint, subnormal, or hyponormal powers

Abstract We show that if a densely defined closable operator A is such the resolvent set of 2 nonempty, then necessarily closed. This result extended to case polynomial . also generalize recent by Sebestyén–Tarcsay concerning converse J. von Neumann. Other interesting consequences are given. One them proof T quasinormal (unbounded) normal for some , normal. Hence closed subnormal itself hyponormal (nonnecessarily bounded) and self‐adjoint coprime numbers p q must be self‐adjoint.