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

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Souheyb Dehimi , Mohammed Hichem Mortad ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.1002/mana.202100390 · OA: W4384281793

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