Asrar Elleuch

University of Sfax | US · Department of Mathematics

Let $(S(t))_{t\geq0}$ and $(T(t))_{t\geq0}$ denote the strongly continuous semigroups of operators in a Banach space $X$. In this paper, we give a sufficient condition guaranteeing that $(S(t))_{t\geq0}$ can be embedded in a $C_{0}$-group on $X$. Moreover, we characterize the demicompactness of $I-(S(t)-T(t))$ for $t>0$. Our theoretical results wil...

Let C be an invertible bounded linear operator in Banach space X. In this paper, we use the concept of relative demicompactness in order to study some properties of an exponentially bounded C-semigroup (T(t))t ≥ 0. More precisely, we prove that the relative demicompactness of T(t) at some positive values of t is equivalent to relative demicompactne...

In this paper, we use the concept of weak demicompactness in order to give some properties for the uniformly continuous cosine families. Our theoretical results will be illustrated by investigating the spectral inclusion for a uniformly continuous cosine family for an upper semi-Fredholm spectrum.

In this paper, we establish some properties for a uniformly continuous cosine family (C(t))t∈R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(C(t))_{t\in \mathbb {R}}$...

Meyer-Nieberg in (Banach Lattices, Springer-Verlag, Berlin, Heidelberg, New York, 1991) present some characterizations of the class of order weakly compact operators. The main focus of this paper is to invest these results in order to introduce the order weakly demicompact operators. Suppose that E is a Banach lattice. An operator T from E into E i...

In this paper, we establish some new spectral properties of bounded operators acting in Banach spaces by means of the concept of quasi-compact operators. Furthermore, we discuss the incidence of some perturbation results on the description of some spectra.

Let (U(t))t≥0 be a strongly continuous semigroup of bounded linear operators on a Banach space X and B be a bounded operator on X. In this paper, we develop some aspects of the theory of semigroup for which U(t)B (respectively, BU(t), BU(t)B) is demicompact for some (respectively, every) t>0. In addition, we study the demicompactness of similar, su...

In this paper, we outline a new approach to the study of structured Schechter and structured Browder essential pseudospectra of closed densely defined linear operators on infinite dimensional Banach spaces via the concept of the measure of noncompactness and the measure of non strict-singularity. Furthermore, we investigate the structured Wolf, str...

In this paper, we concern ourselves with essential spectra of an operator A which is subjected to structured perturbation of the form A → A + CDB where B, C are given bounded operators and D is unknown disturbance operator that satisfies ||D|| < ε for a given ε > 0. Thereby, we investigate the structured essential pseudospectra of the sum of two op...

This paper deals with the spectral properties of multidimensional transport equations with bounce-back boundary conditions arising in L p -spaces \((1 \leq p <\infty )\). These properties are closely related to the large dependent solutions of transport equations. An adequate assumption allows us to investigate the uniform stability of solutions fo...