Unbounded operators having self-adjoint or normal powers and some related results
We show that a densely defined closable operator $ A $ such that the resolvent set of $ A^
2$ is not empty is necessarily closed. This result is then extended to the case of a
polynomial $ p (A) $. We also generalize a recent result by Sebesty\'en-Tarcsay concerning
the converse of a result by J. von Neumann. Other interesting consequences are also given,
one of them being a proof that if $ T $ is a quasinormal (unbounded) operator such that $ T^
n $ is normal for some $ n\geq2 $, then $ T $ is normal. By a recent result by Pietrzycki …
2$ is not empty is necessarily closed. This result is then extended to the case of a
polynomial $ p (A) $. We also generalize a recent result by Sebesty\'en-Tarcsay concerning
the converse of a result by J. von Neumann. Other interesting consequences are also given,
one of them being a proof that if $ T $ is a quasinormal (unbounded) operator such that $ T^
n $ is normal for some $ n\geq2 $, then $ T $ is normal. By a recent result by Pietrzycki …
以上显示的是最相近的搜索结果。 查看全部搜索结果