Sid Ahmed Ould Ahmed Mahmoud
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View article: A Structural Study of Generalized [m,C]-Symmetric Extension Operators
A Structural Study of Generalized [m,C]-Symmetric Extension Operators Open
This manuscript introduces and investigates a new class of operators, termedn-quasi-[m,C]-symmetric operators, which generalize and extend the existing notions of [m,C]-symmetric and n-quasi-[m,C]-isometric operators. Specifically, given a…
View article: Structural properties of 2-C-normal operators
Structural properties of 2-C-normal operators Open
In this paper, we introduce and study a new class of bounded linear operators on complex Hilbert spaces, which we call 2-C-normal operators. This class is inspired by and closely related to the notion of 2-normal operators, with additional…
View article: EXPLORING THE SPECTRAL PROPERTIES OF MULTIVARIABLE (m; n)-ISOSYMMETRIC OPERATORS
EXPLORING THE SPECTRAL PROPERTIES OF MULTIVARIABLE (m; n)-ISOSYMMETRIC OPERATORS Open
Drawing from recent advancements in the study of m-isometric and n-symmetric completely positive operators on Hilbert spaces, this paper introduces the concept of (m; n)- isosymmetric multivariable operators. This new class of operators se…
View article: Toral $(m,C)$-isometric multivariable operators
Toral $(m,C)$-isometric multivariable operators Open
In recent years, various aspects of the problem related to the generalization of the class of m -isometries of commuting tuples of operators in Hilbert spaces have appeared in the literature. Let us mention, for example, $(n_{1},\ldots ,n_…
View article: M-hyponormality in several variables operator theory
M-hyponormality in several variables operator theory Open
In recent years, the study of bounded linear operators in several variables has received great interest from many authors, including the second author’s previous contributions. In our present work, we define a new class of multivariable op…
View article: Similarity of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:msub><a:mrow><a:mi>C</a:mi></a:mrow><a:mrow><a:mn>1</a:mn></a:mrow></a:msub></a:math>: Operators and the Hyperinvariant Subspace Problem
Similarity of C1: Operators and the Hyperinvariant Subspace Problem Open
In the present paper, we first show that the existence of the solutions of the operator equation S∗XT=X is related to the similarity of operators of class C1. , and then we give a sufficient condition for the existence of nontrivial hyperi…
View article: On $k$-quasi-$(m,n,\mathbf{C})$-isosymmetric operators
On $k$-quasi-$(m,n,\mathbf{C})$-isosymmetric operators Open
We study the set of $k$-quasi-$(m,n,\mathbf{C})$-isosymmetric operators. This family extends the set of $(m,,n,\mathbf{C})$-isosymmetric operators. In the present article, we give operator matrix representation of $k$-quasi-$(m,,n,\mathbf{…
View article: On $ (n_1, \cdots, n_m) $-hyponormal tuples of Hilbert space operators
On $ (n_1, \cdots, n_m) $-hyponormal tuples of Hilbert space operators Open
This paper introduces a new class of multivariable operators called $ (n_1, \cdots, n_m) $-hyponormal tuples, which combine joint normal and joint hyponormal operators. A tuple of operators $ \mathcal{Q} = (\mathcal{Q}_1, \; \cdots, \mathc…
View article: New extension of quasi-$ M $-hypnormal operators
New extension of quasi-$ M $-hypnormal operators Open
This study introduces a new class of operators called polynomilally quasi-$ M $-hyponormal, which combining $ M $-hyponormal, quasi-$ M $-hyponormal, and $ k $-quasi-$ M $-hyponormal operators. We will demonstrate several properties of thi…
View article: On the (α, β)-Euclidean operator radius and its applications
On the (α, β)-Euclidean operator radius and its applications Open
Our aim in this paper is to introduce a new norm of n-tuple operators which generalizes the (?,?)-norm on the space of all bounded linear operators on a complex Hilbert space due to Sain et al. (Ann. Funct. Anal. 12:51 (2021)). We introduc…
View article: Optimal control problems governed by a class of nonlinear systems
Optimal control problems governed by a class of nonlinear systems Open
This article suggested a solution to a flow control problem governed by a class of nonlinear systems called bilinear systems. The problem was initially well-posed, and after it was established that an optimal control solution existed, its …
View article: n-Quasi-m-Complex Symmetric Transformations
n-Quasi-m-Complex Symmetric Transformations Open
Our aim in this study is to consider a generalization of the concept of m-complex symmetric transformations to n-quasi-m-complex symmetric transformations. A map S∈B(Y) is said to be an n-quasi-m-complex symmetric transformation if there e…
View article: Spectral properties of (m;n)-isosymmetric multivariable operators
Spectral properties of (m;n)-isosymmetric multivariable operators Open
Inspired by recent works on $m$-isometric and $n$-symmetric multivariables operators on Hilbert spaces, in this paper we introduce the class of $(m, n)$-isosymmetric multivariables operators. This new class of operators emerges as a genera…
View article: (N1,..., nd)-quasi-(p, q)-isometric commuting tuple of operators
(N1,..., nd)-quasi-(p, q)-isometric commuting tuple of operators Open
In this work we construct the concept based on the extension of n-quasi-p-isometric operators of a single operator studied in [11, 14] to the multi-dimentional operators. we are introducing some new interesting results of these family of t…
View article: Class of operators related to a $(m,C)$-isometric tuple of commuting operators
Class of operators related to a $(m,C)$-isometric tuple of commuting operators Open
This paper is concerned with studying a new class of multivariable commuting operators know as left $(m,C)$ -invertible p -tuples and related to a given conjugation transformation C on a Hilbert space $\mathcal{Y}$ . Some structura…
View article: <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mfenced open="(" close=")" separators="|"> <a:mrow> <a:mi>α</a:mi> <a:mo>,</a:mo> <a:mi>β</a:mi> </a:mrow> </a:mfenced> </a:math>-Normal Operators in Several Variables
α , β -Normal Operators in Several Variables Open
We consider an extension of the concept of α , β -normal operators in single variable operator to tuples of operators, similar to those extensions of the concepts of normality to joint normality, hyponormality to joint hyponormality,…
View article: (m,∞)-expansive and (m,∞)-contractive commuting tuple of operators on a Banach space
(m,∞)-expansive and (m,∞)-contractive commuting tuple of operators on a Banach space Open
For a d-tuple of commuting operators S := (S1,..., Sd) ? B[X]d, m ? N and p ? (0,?), we define Q(p) m (S;u) := ? 0?k?m (-1)k (m k) (???Nd0 |?| = k k!/? ||S?u||p). As a natural extension of the concepts of (m,p)-expansive and (m,p)-contract…
View article: k-quasi-A-paranormal operators in semi-Hilbertian spaces
k-quasi-A-paranormal operators in semi-Hilbertian spaces Open
In this paper, we introduce and analyze a new class of generalized paranormal operators, namely k -quasi-A -paranormal operators for a bounded linear operator acting on a complex Hilbert space H when an additional semi-inner product induce…
View article: On $(n,m)$-$A$-normal and $(n,m)$-$A$-quasinormal semi-Hilbertian space operators
On $(n,m)$-$A$-normal and $(n,m)$-$A$-quasinormal semi-Hilbertian space operators Open
The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces, i.e. spaces generated by positive semi-definite sesquilinear forms. Let ${\mathcal H}$ be a Hilbert space and let $A$ be a positive boun…
View article: On m-quasi-totally-(α,β)-normal operators
On m-quasi-totally-(α,β)-normal operators Open
An operator S acting on a Hilbert space is called m -quasi-totally-(α,β ) -normalfor a natural number m and for all λ ∈ C .m -quasi-totally-(α,β ) -normal operator is equivalent to the study of mutual majorization between (S -λ )S m and (S…
View article: On the class of $k$-quasi-$(n,m)$-power normal operators
On the class of $k$-quasi-$(n,m)$-power normal operators Open
We introduce a family of operators called the family of $k$-quasi-$(n,m)$-power normal operators. Such family includes normal, $n$-normal and $(n,m)$-power normal operators. An operator $T \in {\mathcal B}({\mathcal H})$ is said to be $k$-…
View article: Davis–Wielandt shells of semi-Hilbertian space operators and its applications
Davis–Wielandt shells of semi-Hilbertian space operators and its applications Open
View article: (m,q)-isometric and (m,∞)-isometric tuples of commutative mappings on a metric space
(m,q)-isometric and (m,∞)-isometric tuples of commutative mappings on a metric space Open
In this paper, we introduce new concepts of (m,q)-isometries and (m,?)-isometries tuples of commutative mappings on metrics spaces. We discuss the most interesting results concerning this class of mappings obtained form the idea of general…
View article: On the class of n-power D-m-quasi-normal operators on Hilbert spaces
On the class of n-power D-m-quasi-normal operators on Hilbert spaces Open
As a continuation of our previous work [22], this paper is devoted to the study for further properties of the class of (n,m) -power D -normal operators( [(n,m)DN] ) and introduce some classes of operators on Hilbert space called Dm -quasi-…
View article: Classes of operators related to m-isometric operators
Classes of operators related to m-isometric operators Open
Isometries played a pivotal role in the development of operator theory, in particular with the theory of contractions and polar decompositions and has been widely studied due to its fundamental importance in the theory of stochastic proces…
View article: Some results on higher orders quasi-isometries
Some results on higher orders quasi-isometries Open
The purpose of the present paper is to pursue further study of a class of linear bounded operators, known as $n$-quasi-$m$-isometric operators acting on an infinite complex separable Hilbert space ${\mathcal H}$. We give an equivalent cond…
View article: $$(\alpha ,\beta )$$-A-Normal operators in semi-Hilbertian spaces
$$(\alpha ,\beta )$$-A-Normal operators in semi-Hilbertian spaces Open
View article: On the classes of (n,m)-power D-normal and (n,m)-power D-quasi-normal operators
On the classes of (n,m)-power D-normal and (n,m)-power D-quasi-normal operators Open
This paper is devoted to the study of some new classes of operators on Hilbert space called (n,m) -power D -normal [(n,m)DN] and (n,m) -power D -quasi-normal [(n,m)DQN] , associated with a Drazin invertible operator using its Drazin invers…
View article: (A,m)-Symmetric commuting tuples of operators on a Hilbert space
(A,m)-Symmetric commuting tuples of operators on a Hilbert space Open
Let T = (T 1 ,••• ,T d ) and A be a commuting d -tuple of operators and a positive operator on a complex Hilbert space, respectively.We introduce an (A,m) -symmetric commuting tuple of operators and characterize the joint approximate point…
View article: $(α,β)$-A-Normal Operators in Semi-Hilbertian Spaces
$(α,β)$-A-Normal Operators in Semi-Hilbertian Spaces Open
In this paper we introduce and prove some properties of $(α;β)$-normal operators according to semi-Hilbertian space structures. Furthermore we s,ate various inequalities between the A-operator norm and A-numerical radius of $(α,β)$-normal …