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Mohammed Benharrat

Publications and source records attributed to Mohammed Benharrat.

11 recordsLinked to original sources
arXiv2026

Harnack parts for 5-by-5 truncated shift with numerical radius one

We provide a complete description of the Harnack part for normalized truncated shift of size five with numerical radius one. We prove that any operator in this Harnack component must assume one of two distinct forms: either it belongs to the unitary orbit of the shift, thereby preserving its norm, or it is a structured nilpotent matrix with a different norm. Using polynomial methods derived from the kernel conditions, we establish that any element is necessarily nilpotent with same order of the truncated shift. These results reveal that the Harnack equivalence class exhibits a significantly richer algebraic structure in dimension five than previously observed in lower-dimensional cases.

math.FA↗
arXiv2026

Some Sharp bounds for the generalized Davis-Wielandt radius

This paper presents a study of the generalized Davis-Wielandt radius of Hilbert space operators. New lower bounds for the generalized Davis-Wielandt radius and numerical radius are provided. An alternative of the triangular inequality for operators is also derived.

math.FA↗
arXiv2021

The Moore-Penrose inverse of accretive operators with application to quadratic operator pencils

We establish some relationships between an m-accretive operator and its Moore-Penorse inverse. We derive some perturbation result of the Moore-Penorse inverse of a maximal accretive operator. As an application we give a factorization theorem for a quadratic pencil of accretive operators. Also, we study a result of existence, uniqueness, and maximal regularity of the strict solution for complete abstract second order differential equation. Illustrative examples are also given.

math.FA↗
arXiv2021

On the circular numerical range of 5-by-5 partial isometries

We prove, in some cases in term of kippenhahn curve, that if 5-by-5 partial isometry whose numerical range is a circular disc then its center is must be the origin. This gives a partial affirmative answer of the Conjecture 5.1. of [H. l. Gau et al., Linear and Multilinear Algebra, 64 (1) 2016, 14--35.], for the five dimensional case.

math.FA↗
arXiv2020

A perturbation result of m-accretive linear operators in Hilbert spaces

A new sufficient condition is given for the sum of linear m-accretive operator and accretive operator one in a Hilbert space to be m-accretive. As an application, an extended result to the operator-norm error bound estimate for the exponential Trotter-Kato product formula is given.

math.FA↗
arXiv2019

Harnack parts for some truncated shifts

The purpose of this paper is to analysis the Harnack part of some truncated shifts whose $ρ$-numerical radius equal one in the finite dimensional case. As pointed out in Theorem 1.17 [12], a key point is to describe the null spaces of the $ρ$-operatorial kernel of these truncated shifts. We establish two fundamental results in this direction and some applications are also given.

math.FA↗
arXiv2019

Right and left quotient of two bounded operators on Hilbert spaces

We define a left quotient as well as a right quotient of two bounded operators between Hilbert spaces, and we parametrize these two concepts using the Moore-Penrose inverse. In particular, we show that the adjoint of a left quotient is a right quotient and conversely. An explicit formulae for computing left (resp. right) quotient which correspond to adjoint, sum, and product of given left (resp. right) quotient of two bounded operators are also shown.

math.SP↗
arXiv2016

HARNACK parts of $ρ$-Contractions

The purpose of this paper is to describe the Harnack parts for the operators of class C $ρ$ ($ρ$ \textgreater{} 0) on Hilbert spaces which were introduced by B. Sz. Nagy and C. Foias in [25]. More precisely, we study Harnack parts of operators with $ρ$-numerical radius one. The case of operators with $ρ$-numerical radius strictly less than 1 was described in [10]. We obtain a general criterion for compact $ρ$-contractions to be in the same Harnack part. We give a useful equivalent form of this criterion for usual contractions. Operators with numerical radius one received also a particular attention. Moreover, we study many properties of Harnack equivalence in the general case.

math.FA↗
arXiv2016

Left and right generalized Drazin invertible operators and Local spectral theory

In this paper, we give some characterizations of the left and right generalized Drazin invertible bounded operators in Banach spaces by means of the single-valued extension property (SVEP). In particular, we show that a bounded operator is left (resp. right) generalized Drazin invertible if and only if admits a generalized Kato decomposition and has the SVEP at 0 (resp. it admits a generalized Kato decomposition and its adjoint has the SVEP at 0. In addition, we prove that both of the left and the right generalized Drazin operators are invariant under additive commuting finite rank perturbations. Furthermore, we investigate the transmission of some local spectral properties from a bounded linear operator, as the SVEP, Dunford property $(C)$, and property $(β)$, to its generalized Drazin inverse.

math.SP↗
arXiv2014

Optimal control with time-delays via the penalty method

We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general optimal control problem with time delays is considered. Main result gives a convergence theorem, allowing to obtain a solution to the delayed optimal control problem by considering a sequence of delayed problems of the calculus of variations.

math.OC↗