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Abdelaziz Tajmouati

Publications and source records attributed to Abdelaziz Tajmouati.

At least 19 recordsLinked to original sources
arXiv2021

Local Ergodic Theorems for C0-Semigroups

Let $\{T(t)\}_{t\geq 0}$ be a $C_0$-semigroup of bounded linear operators on the Banach space ${X}$ into itself and let $A$ be their infinitesimal generator. In this paper, we show that if $T(t)$ is uniformly ergodic, then $A$ does not have the single valued extension property, which implies that $A$ must have a nonempty interior of the point spectrum. Furthermore, we introduce the local mean ergodic for $C_0$-semigroup $T(t)$ at a vector $x\in X$ and we establish some conditions implying that $T(t)$ is a local mean ergodic at $x$.

math.FA↗
arXiv2019

Generalized Drazin-Riesz Invertibility for Operators Matrices

Let $A\in\mathcal{B}(X)$, $B\in\mathcal{B}(Y)$ and $C\in\mathcal{B}(Y,X)$ where $X$ and $Y$ are infinite Banach or Hilbert spaces. Let $M_{C}=\begin{pmatrix} A & C\cr 0 & B \end{pmatrix}$ be $2\times 2$ upper triangular operator matrix acting on $X\oplus Y$. In this paper, we consider some necessary and sufficient conditions for $M_{C}$ to be generalized Drazin-Riesz invertible. Furthermore, the set $\bigcap_{C\in \mathcal{B}(Y,X)}σ_{gDR}(M_{C})$ will be investigated and their relation between $\bigcap_{C\in \mathcal{B}(Y,X)}σ_{b}(M_{C})$ will be studied, where $σ_{gDR}(M_{C})$ and $σ_{b}(M_{C})$ denote the generalized Drazin-Riesz spectrum and the Browder spectrum, respectively.

math.FA↗
arXiv2018

On Orbit Reflexive Tuple of Operators And Weak Orbit Reflexivity

In this paper we give a various conditions for which the tuple $\mathcal{T} = (T_{1} , T_{2} , ... , T_{n})$ of commutative bounded linear operators on an infinite dimensional ( real , complex ) Banach space X is orbit reflexive. After we introduce the notion of weak orbit reflexive operator and we show some results.

math.FA↗
arXiv2018

Limit Points for Browder Spectrum of Operator Matrices

Let $A\in \mathcal{B}(X)$ and $B\in \mathcal{B}(Y)$, where $X$ and $Y$ are Banach spaces, and let $M_{C}$ be an operator acting on $X\oplus Y$ given by $M_C=\begin{pmatrix} A & C \\ 0 & B \\ \end{pmatrix}$. We investigate the limit point set of the Browder spectrum of $M_{C}$. It is shown that $$ acc σ_{b}(M_C)\cup W_{acc σ_{b}}= acc σ_{b}(A)\cup acc σ_{b}(B)$$ where $W_{acc σ_{b}}$ is a subsets of $ accσ_{*}(B)\cap accσ_{*}(A)$ and a union of certain holes in $ acc σ_{b}(M_C)$. Furthermore, several sufficient conditions for $accσ_{b}(M_C)=accσ_{b}(A)\cup accσ_{b}(B)$ holds for every $C\in \mathcal{B}(Y,X)$ are given.

math.FA↗
arXiv2018

Spectral mapping theorems of differentiable C0 semigroups

Let $(T(t))_{t\geq 0}$ be a $C_0$ semigroup on a Banach space $X$ with infinitesimal generator $A$. In this work, we give conditions for which the spectral mapping theorem $σ_{*}(T(t))\backslash \{0\}=\{e^{λs}, λ\inσ_{*}(A)\}$ holds, where $σ_*$ can be equal to the essential, Browder and Kato spectrum. Also, we will be interested in the relations between the spectrum of $A$ and the spectrum of the nth derivative $T(t)^{(n)}$ of a differentiable $C_0$ semigroup $(T(t))_{t\geq0}$.

math.SP↗
arXiv2018

Riesz Decomposition Relative to C*-Algebra Homomorphisms

The aim of the present work is to study the Riesz decomposition relative to a C*-algebra homomorphism T : A --> B. We prove that under some conditions on T, T-Riesz elements can be decomposed into the sum of almost T-null element and quasi-nilpotent element. Also the so-called polyno- mial T-Riesz and generalized T-Riesz decompositions will be discussed.

math.SP↗
arXiv2018

Problem of Descent Spectrum Equality

Let $\mathcal{B}(X)$ be the algebra of all bounded operators acting on an infinite dimensional complex Banach space $X$. We say that an operator $T \in \mathcal{B}(X)$ satisfies the problem of descent spectrum equality, if the descent spectrum of $T$ as an operator coincides with the descent spectrum of $T$ as an element of the algebra of all bounded linear operators on $X$. In this paper we are interested in the problem of descent spectrum equality . Specifically, the problem is to consider the following question: Let $T \in \mathcal{B}(X)$ such that $σ(T)$ has non empty interior, under which condition on $T$ does $σ_{desc}(T)=σ_{desc}(T, \mathcal{B}(X))$ ?

math.SP↗
arXiv2018

Essential Descent Spectrum Equality

A bounded operator $T$ in a Banach space $X$ is said to satisfy the essential descent spectrum equality, if the descent spectrum of $T$ as an operator on $X$ coincides with the essential descent spectrum of $T$. In this note, we give some conditions under which the equality $σ_{desc}(T) = σ^e_{desc}(T)$ holds for a single operator $T$.

math.SP↗
arXiv2017

Spectra Originated from Fredholm Theory and Browder's Theorem

We give a new characterization of Browders theorem through equality between the pseudo B-Weyl spectrum and the generalized Drazin spectrum. Also, we will give conditions under which pseudo B-Fredholm and pseudo B-Weyl spectrum introduced in [11] and [30] become stable under commuting Riesz perturbations.

math.SP↗
arXiv2016

ON λ-Commuting Operators

In this paper, we study the operator equation $AB=λBA$ for a bounded operator $A,B$ on a complex Hilbert space. We focus on algebraic relations between different operators that include normal, $M$-hyponormal, quasi $*$-paranormal and other classes.

math.SP↗
arXiv2016

Pseudo B-Fredholm Operators and Spectral Theory

In this paper, we show that every pseudo B-Fredholm operator is a pseudo Fredholm operator. Afterwards, we prove that the pseudo B-Weyl spectrum is empty if and only if the pseudo B-Fredholm spectrum is empty. Also, we study a symmetric difference between some parts of the spectrum.

math.SP↗
arXiv2016

Generalized Kato Decomposition For Operator Matrices and SVEP

In this paper, we show that for a bounded linear operator $T$, the corresponding generalized Kato decomposition spectrum $σ_{gK}(T)$ satisfies the equality $σ_{gD}(T)=σ_{gK}(T)\cup (S(T)\cup S(T^*))$ where $σ_{gD} (T ) $ is the generalized Drazin spectrum of $T$ and $S(T )$ (resp., $S(T^*)$ is the set where T (resp., $T^*$) fails to have SVEP. As application, we give sufficient conditions which assure that the generalized Kato decomposition spectrum of an upper triangular operator matrices is the union of its diagonal entries spectra. Moreover, some applications are given.

math.SP↗