M. HERAIZ Toufik

MCB

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Department

BASE COMMON ST Departement ST

Research Interests

Functional Analysis Operator Theory Spectrum Theory PDE

Contact Info

University of M'Sila, Algeria

Email : toufik.heraiz@univ-msila.dz

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Recent Publications

2024-12-16

NEW RESULTS OF ESSENTIAL APPROXIMATE AND DEFECT POINT SPECTRUM BY USING THE GAP CONVERGENCE

This paper focuses on exploring the relationship between the essential approximate point spectrum (and the essential defect spectrum) of a sequence of closed
linear operators (Tn)n2N acting on a Banach space X, and the corresponding spectra
of a linear operator T on X. We examine this relationship under both generalized
convergence and compact convergence conditions for the sequence (Tn)n2N converging
to T.
Citation

M. HERAIZ Toufik, Aymen Ammar, Aref Jeribi, , (2024-12-16), "NEW RESULTS OF ESSENTIAL APPROXIMATE AND DEFECT POINT SPECTRUM BY USING THE GAP CONVERGENCE", [national] Facta Universitatis serie MI , University of Nis

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2023-12-06

The Gap topology and the sequence of closed linear operators

While the distance between two bounded linear operators is measured as the norm of their difference, the distance between two unbounded linear operators is measured by different ways. One of the possibilties is the gap between their graphs
Citation

M. HERAIZ Toufik, (2023-12-06), "The Gap topology and the sequence of closed linear operators", [international] IWAM02 Constantine2023 , Constantine Algeria

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2022

THE S-v-CONVERGENCE OF A SEQUENCE OF BOUNDED LINEAR OPERATORS AND THE S-v-CONTINUITY

This paper is devoted to introduce and study a new mode of convergence of a sequence of bounded linear operators in Banach space, which is the S-ν-convergence. Moreover, we study the S-ν-continuity of the Weyl essential spectrum.
Citation

M. HERAIZ Toufik, (2022), "THE S-v-CONVERGENCE OF A SEQUENCE OF BOUNDED LINEAR OPERATORS AND THE S-v-CONTINUITY", [international] 6th International Conference of Operatot Theory ICOT 2022 , Sousse, Tunisia

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The Pherturbation teory of a equence of boune linea operator an the -V-Converece

The spectrum of a linear operator is one of the most useful objects in functional analysis. However, since exact computations of the spectrum are almost always impossible, it is relevant to know the spectrum or any of its parts in approximate way. Several authors have studied this problem and other related topics using various types of convergence in L(X). There are several notions of convergence of a sequence of operators which yield spectral results: the norm convergence (<cite>Burlando</cite>, <cite>Conway1</cite>, <cite>Conway2</cite>, <cite>Dordevic</cite>, <cite>Djordj1</cite>, <cite>Djordj2</cite>, <cite>Duggal</cite>, <cite>Newburgh</cite>, <cite>Sanchez1</cite>, <cite>Sanchez2</cite>,<cite>Schmoeger1</cite>), collectively compact convergence (<cite>Philip</cite>), compact convergence and regular convergence (<cite>Anselon Ansorge</cite>), stable and strongly stable convergence (<cite>Chatel</cite>), resolvent operator convergence (<cite>Limay</cite>)
Citation

M. HERAIZ Toufik, (2022), "The Pherturbation teory of a equence of boune linea operator an the -V-Converece", [international] The Firt internationa workop on applie Matematic IWAM 2022 , Constantine Algeria

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On the v-continuity of the essenttial spectrum of 3*3 block operators matrices

This work is devoted to extend the results of A. Ammar in (<cite>Aymen</cite>)in 2×2 block operator matrices to 3×3 block operator matrices.
Citation

M. HERAIZ Toufik, (2022), "On the v-continuity of the essenttial spectrum of 3*3 block operators matrices", [national] Third National Mathematics Seminar 2022 , Constantine Algeria

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On The Essential Spectrum Of a Sequence Of 3*3 Block Operatoor Matrices

A. Ammar studied the spectrum continuity of the Weyl and the Wolf essential spectrum of 2×2 block operator matrices using the ν-convergence (<cite>Aymen</cite>), it is the result that we want to extend in the next section to 3×3 block operator matrices. Particularly we focus on the relationship between the ν-continuity of 3×3 block operator matrices and the ν-continuity of its components.
Citation

M. HERAIZ Toufik, (2022), "On The Essential Spectrum Of a Sequence Of 3*3 Block Operatoor Matrices", [international] 6th International of Mathematics ICOM , Istanbul Turky

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2016

ESSENTIAL APPROXIMATE POINT, AND ESSENTIAL DEFECT SPECTRUM OF A SEQUENCE OF LINEAR OPERATORS IN BANACH SPACES

The central objective of this work is to make an extensive study about the essential approximate point spectrum, noted σ_{eap}(.), and the essential defect spectrum, noted σ_{eδ}(.), of a sequence of linear operators in Banach spaces. According to the convergence sense of the sequence of operators, our work may be devised in two parts, the first is concerned on the case of a sequence of closed linear operators T_{n} converges in the generalized sense to a closed linear operator T (see Definition <ref>definition33</ref>), and the second is concerned on the case of a sequence of bounded linear operators T_{n} converges compactly to a bounded linear operator T (see Definition <ref>Definition2</ref>).
Citation

M. HERAIZ Toufik, (2016), "ESSENTIAL APPROXIMATE POINT, AND ESSENTIAL DEFECT SPECTRUM OF A SEQUENCE OF LINEAR OPERATORS IN BANACH SPACES", [international] CITO 2016 , Elchahid Hamma Lahdar Univerity- Eloued Algeria

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On Composition of semi-regular operattors

In this thesis whenever, A and B are semi regular operators does not imply, in general, that the product AB is semi regular. We do, however, give conditions under which the above implication is valid.
Citation

M. HERAIZ Toufik, (2016), "On Composition of semi-regular operattors", [international] International Conference of The Euro-Mahreb Laborattory Of Mathematics And their Interaction , sFax Tunisia

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