17 citations · 64 across the 32 of their papers we have counts for
6 papers · 1 filter
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…
Unbounded operators: (square) roots, nilpotence, closability and some related invertibility results
Mohammed Hichem Mortad
In this paper, we are mainly concerned with studying arbitrary unbounded square roots of linear operators as well as some of their basic properties. The paper contains many example…
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…
Yet another generalization of the Fuglede-Putnam theorem to unbounded operators
Mohammed Hichem Mortad
In this note, we give the most natural (perhaps the simplest ever) generalization of the Fuglede-Putnam theorem where all operators involved are unbounded.
A closed densely defined operator such that both and are injective and paranormal yet is not normal
Mohammed Hichem Mortad
In this note, we give an example of a densely defined closed one-to-one paranormal operator whose adjoint is also injective and paranormal, but fails to be normal.
Simple examples of non closable paranormal operators
Mohammed Hichem Mortad
In this note, we give an example of a densely defined non-closable paranormal operator. Then, we give another example of a densely defined closable paranormal operator whose closur…