M. YAHI Rachid

MCA

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Department

BASE COMMON ST Departement ST

Research Interests

Functional analysis

Contact Info

University of M'Sila, Algeria

Email : rachid.yahi@univ-msila.dz

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Recent Publications

2024-11-24

LIPSCHITZ CLOSED INJECTIVE HULL IDEALS AND LIPSCHITZ INTERPOLATIVE IDEALS

In this paper we present two constructions: the Lipschitz closed injective
hull ideals and the Lipschitz interpolative ideals of a Lipschitz operator ideal. These
procedures aim to construct new Lipschitz operator ideals between pointed metric
spaces and Banach spaces. The new ideals are characterized by specific criteria
that determine whether a Lipschitz operator belongs to them, using summability
properties and interpolation formulas.
Citation

M. YAHI Rachid, (2024-11-24), "LIPSCHITZ CLOSED INJECTIVE HULL IDEALS AND LIPSCHITZ INTERPOLATIVE IDEALS", [national] Quaestiones Mathematicae , Taylor & Francis

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2024-11-20

Multilinear p-th power factorable operators

The generalization of operator ideals to
ideals of multilinear operators is a problem recently carried
out for some kind of operators, Following this trend
we extend the ideal of $\mathcal{F}_{p}$-factorable
operators to the multilinear case.
Citation

M. YAHI Rachid, (2024-11-20), "Multilinear p-th power factorable operators", [international] 1st International Conference Mohand Moussaoui on Applied Mathematics and Modeling , جامعىة قالمة

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2024-10-23

The closed injective hull of a two Lipschitz operatorsideals

In this talk we present two methods for establishing a linear op-
erators ideals: The Closed Injective hull and the interpolative method, related

to an operator ideal, in order to get an new classes of linear operators ideals,
some examples are given, modeled the class of (p, σ)-absolutely continuous
operators.
Citation

M. YAHI Rachid, (2024-10-23), "The closed injective hull of a two Lipschitz operatorsideals", [national] 8 th M’Sila conference on Mathematical Analysis , University of M'sila

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THE CLOSED INJECTIVE HULL of Two Lipschitz OPERATOR IDEAL

In this talk we present two methods for establishing a linear operators ideals: The Closed Injective hull and the interpolative method, related to an operator ideal, in order to get an new classes of linear operators ideals, some examples are given, modeled the class of $(p,\sigma)$-absolutely continuous operators.
Citation

M. YAHI Rachid, (2024-10-23), "THE CLOSED INJECTIVE HULL of Two Lipschitz OPERATOR IDEAL", [national] 8th M’sila Conference on Mathematical Analysis (MCMA’2024) Banach spaces and operator theory October 23rd, 2024. M’sila, Algeria , .M’sila, Algeria

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2024-08-25

The Lipschitz K{p,q} Compactness and LipschitzK{p,q}-Null Sequences.

In this presentation, we deal with one of the most important topics in functional analysis, namely $\mathcal{I}$-Compact set and $\mathcal{I}$-null sequence we introduce some results related to Lipschitz relatively \( K_{p,q} \)-compact sets and Lipschitz$ K_{p,q} $-null sequence..
Citation

M. YAHI Rachid, (2024-08-25), "The Lipschitz K{p,q} Compactness and LipschitzK{p,q}-Null Sequences.", [international] 24 International Pure Mathematics Conference 2024 from 23 to 25 August 2024, Islamabad, Pakistan. , Islamabad, Pakistan.

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2024-07-06

Ideal of multilinear -factorable operators and applications

In the present paper we introduce a method for generating ideals of linear and multilinear operators from what we call generalized left and right operator ideals, that we discuss with p-th power factorable, p-convex and q-concave operators. Then we combine this method with the Factorization Ideal method, that construct multilinear operators, in order to introduce the ideal of multilinear -factorable operators as an example of an ideal generated by means of our method. Finally, we investigate its relation with multilinear summing operators.
Citation

M. YAHI Rachid, D., Galdames-Bravo, , (2024-07-06), "Ideal of multilinear -factorable operators and applications", [national] Advances in Operator Theory , Springer International Publishing

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2023-12-19

STRONGLY (p; sigma) ABSOLUTELY LIPSCHITZ OPERATORS

In this talk we introduce the class of Strongly (p; ) absolutely Lipschitz operators
as a conjugate of the classes of (p; ) absolutely Lipschitz operators. The Domination
theorem and Pietsch factorization theorem related to this classes are given. .
Keywords:Lipschitz operator, Strongly (p; ) absolutely Lipschitz operators, Pietsch factorization
theorem, Pietsch domination theorem.
Citation

M. YAHI Rachid, (2023-12-19), "STRONGLY (p; sigma) ABSOLUTELY LIPSCHITZ OPERATORS", [national] «The First National Conference on Differential Geometry and Dynamical Systems DGDS 2023, organized by the Department of Mathematics on December 19-20, 2023 in Relizane, Algeria , Département de Mathématiques, Faculté des Sciences et Technologies, Université de Relizane

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2023-07-03

Some Lipschitz operators between Banach spaces

The theory of operator ideals was introduced by Albrecht Pietsch, which is nowadays well established. Many
classes of linear operator ideals are introduced in Lipschitz context (Lipschitz p−summing, Lipschitz p−nuclear,
Lipschitz p−integral, Lipschitz compact, weakly compact,...etc). In this talk we present the lipschitz version
of the ideal of strongly p-summing operators and we give some results.
Citation

M. YAHI Rachid, (2023-07-03), "Some Lipschitz operators between Banach spaces", [international] 7 th International Conference of Mathematical Sciences (ICMS 2023) 5-9 July 2023, Maltepe University, Istanbul, Turkey , Maltepe University, Istanbul, Turkey

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2023-06-02

The approximation property for spaces of Lipschitz functions

The theory of linear operator ideals between normed (or Banach) spaces have
been developed by Albert Pietsch \cite{Pi80}, and it is nowadays well
established. A linear operator ideal $\mathcal{I}$ is a subclass of the
class of all continuous linear operators, such that for every Banach spaces $%
E$ and $F$, the set $\mathcal{I}(E,F)$ is a vector subspace of $\mathcal{L}%
(E,F)$ that is invariant by the composition of linear operators on the right
or and on the left and which contains the linear operators of finite rank. In this work we study the approximation property of Lipschitz mappings
Citation

M. YAHI Rachid, (2023-06-02), "The approximation property for spaces of Lipschitz functions", [international] International Conference of Young Mathematicians June 1–3, 2023 Institute of Mathematics of NAS of Ukraine (online), Kyiv, Ukraine , Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine

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2022

Extrapolation theorems for Lipschitz (p; q)-factorable operators

In this work we present some extrapolation theorems studied by Orlando
Galdames-Bravo , and how to extend this in the lipschitz case, by introducing the
concept of Lipschitz (p, q)-factorable operators
Citation

M. YAHI Rachid, (2022), "Extrapolation theorems for Lipschitz (p; q)-factorable operators", [national] Rencontre d’Analyse Mathématique et ses Applications (RAMA) , جامعة محمد بوضياف مسيلة

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Interpolative Lipschitz operator ideals

Following recent advances in the theory of ideals of Lipschitz mappings, we present (p; sigma)-
absolutely Lipschitz mappings as an interpolating class between Lipschitz mappings and Lipschitz
absolutely p-summing mappings.
Citation

M. YAHI Rachid, (2022), "Interpolative Lipschitz operator ideals", [national] 2nd National Conference on Pure and Applied Mathematics NCPAM’2022, December 18 - 19, 2022, Laghouat, Algeria , جامعةعمار ثليجي الأغواط

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Maurey-Rosenthal type theorems on factorization through Lp-spaces.

There are many classical results relating inequalities for linear operators and factorizations.
Probably, the ones that have found more applications are the nowadays called Maurey-Rosenthal
theorems, and the associated inequalities for obtaining strong factorizations through Lp-spaces
are the ones coming from p-convexity and p-concavity requirements for the operators of the
spaces involved (see [1, 2, 3]).
In this talk we study the Lipschitz version of Maurey-Rosenthal theorems.
Citation

M. YAHI Rachid, (2022), "Maurey-Rosenthal type theorems on factorization through Lp-spaces.", [international] International E-Conference on Mathematical and Statistical Science. , تركيا

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Summability of Sequence Spaces and Lipschitz mappings

Farmer and Johnson introduce the notion of absolute summability for Lipschitz maps, proved a
basic first properties and leave to interested readers a list of open problems (what results about
p-summing operators have analogues for Lipschitz p-summing operators?). Since then, many works
have appeared related to this class of Lipschitz mappings and some of the problems have been
solved.we contribute to the theory of absolutely p-summing Lipschitz mappings by studying the
class of Lipschitz summing mappings whose linear analogue has found its natural place in
the linear operator theory: the class of Lipschitz strongly p-summing mappings. The aim is
to characterize those mappings whose Lipschitz conjugates are absolutely p-summing. We
emphasize the relation of these mappings with the known linear theory using two different
ways: via their linearization and via their Lipschitz conjugates. After giving equivalences for
these operators in terms of a summability inequality and its correspondent domination formula,
we prove that a map T is Lipschitz strongly p-summing if, and only if, its Lipschitz conjugate is absolutely p-summing.
Note that the Lipschitz conjugate is a linear operator, and so relates the new class of
Lipschitz strongly p-summing mappings with the classical theory of absolutely p-summing
linear operators.
Chen-Zheng recently proved that if a Lipschitz mapping T from a pointed metric space X
into a Hilbert space H, with T(0) = 0, is such that T is p′−summing (1 < p ≤ ∞), then T is
1-summing. We provide another proof of this result by using the concept of strongly Lipschitz
p-summing. We end this chapter with a factorization theorem for Lipschitz strongly p-summing
mappings.
Citation

M. YAHI Rachid, (2022), "Summability of Sequence Spaces and Lipschitz mappings", [international] 4th BYMAT Conference – Bringing Young Mathematicians Together , اسبانيا

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2018

Factorization of Lipschitz operators on Banach function spaces

Let (X,d) be a pointed metric space. Let T : X ¿ Y1(µ) and S : X ¿ Y2(µ) be two Lipschitz operators into two Banach function spaces Y1 and Y2 over the same finite measure µ. We show which are the vector norm inequalities that characterize those T and S for which T = Mg ¿ S, for some multiplication operator Mg : Y2 ¿ Y1. Our ideas give rise to Maurey-Rosenthal type factorization results for Lipschitz operators. We provide some applications on the Lipschitz structure of metric subsets of Banach function spaces.
Citation

M. YAHI Rachid, E Dahia, P Rueda, Enrique Alfonso Sánchez Pérez, , (2018), "Factorization of Lipschitz operators on Banach function spaces", [national] Mathematical Inequalities & Applications , Element doo

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2017

(p,σ)-Absolutely Lipschitz operators

Due to recent advances in the theory of ideals of Lipschitz mappings, we introduce (p,σ)-absolutely Lipschitz mappings as an interpolating class between Lipschitz mappings and Lipschitz absolutely p-summing mappings. Among other results, we prove a factorization theorem that provides a reformulation to the one given by Farmer and Johnson for Lipschitz absolutely p-summing mappings.
Citation

M. YAHI Rachid, P. Rueda, , (2017), "(p,σ)-Absolutely Lipschitz operators", [national] Annals of Functional Analysis , Tusi Mathematical Research Group

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2016

Certaines classes d opérateurs générés par une procédure d interpolation

Many classes of linears operator ideals for example the p-summing, p-nuclear, p-integral, compact and weakly compact operators have been developed and studied in the Lipschitz setting by several authors. In this thesis we introduce the notion of Lipschitz operator ideal and some methods of constructions. We show that a number of examples of classes of Lipschitz maps that have appeared in the literature fall within this notion of Lipschitz operator ideal. New classes of Lipschitz operators ideals are introduced and study in our thesis, namely the strongly Lipschitz p-summing operator and -absolutely Lipschitz operator, as an application we studied the approximation property for Lipschitz operator ideals. We finish this thesis by studying the factorization of Lipschitz operators on Banach function spaces.

Keywords : Arens–Eells space, Lipschitz mapping, Lipschitz operator ideal, Lipschitz absolutely p-summing operators, strongly Lipschitz p-summing, -absolutely Lipschitz mappings, Pietsch factorization theorem , Approximation property, Banach function spaces, factorization of operators, multiplication operators.
Citation

M. YAHI Rachid, (2016), "Certaines classes d opérateurs générés par une procédure d interpolation", [national] Université de M'sila

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Absolutely summing Lipschitz conjugates

The aim of this paper is to contribute to the study of summability of Lipschitz mappings by characterizing those Lipschitz mappings whose Lipschitz conjugates are absolutely p-summing, namely the classes of Lipschitz strongly p-summing mappings (1 < p ≤ ∞).
Citation

M. YAHI Rachid, P Rueda, , (2016), "Absolutely summing Lipschitz conjugates", [national] Mediterranean Journal of Mathematics , Springer International Publishing

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Lipschitz operator ideals and the approximation property

We establish the basics of the theory of Lipschitz operator ideals with the aim of recovering several classes of Lipschitz maps related to absolute summability that have been introduced in the literature in the last years. As an application we extend the notion and main results on the approximation property for Banach spaces to the case of metric spaces.
Citation

M. YAHI Rachid, P. Rueda, EA Sánchez-Pérez, , (2016), "Lipschitz operator ideals and the approximation property", [national] Journal of Mathematical Analysis and Applications , Academic Press

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