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math.FA2020★ 3 cited
When Nilpotence Implies the Zeroness of Linear Operators
Nassima Frid, Mohammed Hichem Mortad, Souheyb Dehimi
In this paper, we give conditions forcing nilpotent operators (everywhere bounded or closed) to be null. More precisely, it is mainly shown any closed or everywhere defined bounded…
math.FA2020
Unbounded operators having self-adjoint or normal powers and some related results
Souheyb Dehimi, Mohammed Hichem Mortad
We show that a densely defined closable operator such that the resolvent set of is not empty is necessarily closed. This result is then extended to the case of a polynomi…