M. H. Mortad

activity

20122024

most citedUnbounded Products of Operators and Connections to Dirac-Type Operators

17 citations · 64 across the 32 of their papers we have counts for

collaborators

43 papers

math.FA2024

On the reduction of powers of self-adjoint operators

Salima Kebli, Mohammed Hichem Mortad

Let $T \in B (H)$ be such that $T^{n}$ is self-adjoint for some $n \in N$ with $n \geq 3$ . The paper's primary aim is to establish the conditions that lead to the self-adjointnes…

math.GM2023

The square root theorem for positive semidefinite matrices and their monotonicity

Mohamed Amine Aouichaoui, Mohammed Hichem Mortad

In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.

math.FA2022

Certain properties involving the unbounded operators $p (T)$ , $T T^{}$ , and $T^{} T$ ; and some applications to powers and $n t h$ roots of unbounded operators

Mohammed Hichem Mortad

In this paper, we are concerned with conditions under which $[p (T)]^{*} = p ˉ (T^{*})$ , where $p (z)$ is a one-variable complex polynomial, and $T$ is an unbounded, densely defined, an…

math.FA2022

Some properties of the adjoint of the unbounded operators $T T^{}$ and $T^{} T$

Mohammed Hichem Mortad

In this note, we mainly investigate the validity of the identities $(T T^{*})^{*} = T T^{*}$ and $(T^{*} T)^{*} = T^{*} T$ , where $T$ is a densely defined closable (or symmetric) operator.

math.FA2022

On the commutativity of closed symmetric operators

Souheyb Dehimi, Mohammed Hichem Mortad, Ahmed Bachir

In this article, we give conditions guaranteeing the commutativity of a bounded self-adjoint operator with an unbounded closed symmetric operator.

math.FA2022

Unbounded generalizations of the Fuglede-Putnam theorem

Souheyb Dehimi, Mohammed Hichem Mortad, Ahmed Bachir

In this paper, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem.

math.FA2022

On Generalized Powers of Operators

Ahmed Bachir, Mohammed Hichem Mortad, Nawal Ali Sayyaf

In this note, we introduce generalized powers of linear operators. More precisely, operators are not raised to numbers but to other operators. We discuss several properties as rega…

math.FA2022

Unbounded generalizations of the Fuglede-Putnam theorem and applications to the commutativity of self-adjoint operators

Souheyb Dehimi, Mohammed Hichem Mortad, Ahmed Bachir

In this article, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem. As applications, we give conditions guaranteeing the commutativi…

math.FA2021

The sandwich rule for sequences of self-adjoint operators and some applications

Cherifa Chellali, Mohammed Hichem Mortad

In this paper, we mainly deal with sequences of bounded linear operators on Hilbert space. The main result is the so-called squeeze theorem (or sandwich rule) for convergent sequen…

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★ 1 cited

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…

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 $A$ such that the resolvent set of $A^{2}$ is not empty is necessarily closed. This result is then extended to the case of a polynomi…

math.FA2020

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.

math.FA2020

A closed densely defined operator $T$ such that both $T$ and $T^{*}$ are injective and paranormal yet $T$ is not normal

Mohammed Hichem Mortad

In this note, we give an example of a densely defined closed one-to-one paranormal operator $T$ whose adjoint is also injective and paranormal, but $T$ fails to be normal.

math.FA2020★ 3 cited

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…

math.FA2019

On the Operator Equations $A^{n} = A^{*} A$

Souheyb Dehimi, Mohammed Hichem Mortad, Zsigmond Tarcsay

Let $n \in N$ and let $A$ be a closed linear operator (everywhere bounded or unbounded). In this paper, we study (among others) equations of the type $A^{*} A = A^{n}$ where $n\geq…

math.FA2019★ 1 cited

When Nilpotence Implies Normality of Bounded Linear Operators

Nassima Frid, Mohammed Hichem Mortad

In this paper, we give conditions forcing nilpotent matrices (and bounded linear operators in general) to be null or equivalently to be normal. Therefore, a non-zero operator havin…

math.FA2019

The Fuglede Theorem and Some Intertwining Relations

Ikram Fatima Zohra Bensaid, Souheyb Dehimi, Bent Fuglede +1

In this paper, we show a new and classic version of the celebrated Fuglede Theorem in an unbounded setting. A related counterexample is equally presented. In the second strand of t…

math.FA2018

On the triviality of domains of powers and adjoints of closed operators

Mohammed Hichem Mortad

The paper is devoted to counterexamples involving the triviality of domains of products and/or adjoints of densely defined operators.

math.FA2018

Counterexamples Related to Commutators of Unbounded Operators

Mohammed Hichem Mortad

The present paper is exclusively devoted to counterexamples about commutators and self commutators of unbounded operators on a Hilbert space. As a bonus, we provide a simpler count…

math.FA2018

Chernoff Like Counterexamples Related to Unbounded Operators

Souheyb Dehimi, Mohammed Hichem Mortad

In this paper, we give an example of a closed unbounded operator whose square's domain and adjoint's square domain are equal and trivial. Then, we come up with an essentially self-…

math.FA2018

On The Absolute Value of Unbounded Operators

Imene Boucif, Souheyb Dehimi, Mohammed Hichem Mortad

The primary purpose of the present paper is to investigate when relations of the types $∣ A B ∣ = ∣ A ∣∣ B ∣$ , $∣ A \pm B ∣ \leq ∣ A ∣ + ∣ B ∣$ , $∣∣ A ∣ - ∣ B ∣∣ \leq ∣ A \pm B ∣$ and $|\overline{\text{Re} A}|…

math.FA2018

On the Invertibility of the Sum of Operators

Mohammed Hichem Mortad

The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting e…

math.FA2018

On the Existence of Normal Square and Nth Roots of Operators

Mohammed Hichem Mortad

The primary purpose of this paper is to show the existence of normal square and nth roots of some classes of bounded operators on Hilbert spaces. Two interesting simple results hol…

On the reduction of powers of self-adjoint operators

The square root theorem for positive semidefinite matrices and their monotonicity

Certain properties involving the unbounded operators p(T), TT∗, and T∗T; and some applications to powers and nth roots of unbounded operators

Some properties of the adjoint of the unbounded operators TT∗ and T∗T

On the commutativity of closed symmetric operators

Unbounded generalizations of the Fuglede-Putnam theorem

On Generalized Powers of Operators

Unbounded generalizations of the Fuglede-Putnam theorem and applications to the commutativity of self-adjoint operators

The sandwich rule for sequences of self-adjoint operators and some applications

When Nilpotence Implies the Zeroness of Linear Operators

Unbounded operators: (square) roots, nilpotence, closability and some related invertibility results

Unbounded operators having self-adjoint or normal powers and some related results

Yet another generalization of the Fuglede-Putnam theorem to unbounded operators

A closed densely defined operator T such that both T and T∗ are injective and paranormal yet T is not normal

Simple examples of non closable paranormal operators

On the Operator Equations An=A∗A

When Nilpotence Implies Normality of Bounded Linear Operators

The Fuglede Theorem and Some Intertwining Relations

On the triviality of domains of powers and adjoints of closed operators

Counterexamples Related to Commutators of Unbounded Operators

Chernoff Like Counterexamples Related to Unbounded Operators

On The Absolute Value of Unbounded Operators

On the Invertibility of the Sum of Operators

On the Existence of Normal Square and Nth Roots of Operators

Certain properties involving the unbounded operators $p (T)$ , $T T^{}$ , and $T^{} T$ ; and some applications to powers and $n t h$ roots of unbounded operators

Some properties of the adjoint of the unbounded operators $T T^{}$ and $T^{} T$

A closed densely defined operator $T$ such that both $T$ and $T^{*}$ are injective and paranormal yet $T$ is not normal

On the Operator Equations $A^{n} = A^{*} A$