Arafat Abbar

activity

20202026

most citedOn several dynamical properties of shifts acting on directed trees

7 citations · 11 across the 6 of their papers we have counts for

collaborators

8 papers

math.FA2026

On absolutely Cesàro bounded operators

Arafat Abbar, Loris Arnold, Clément Coine

We study $p$ -absolutely Cesàro bounded operators, with particular emphasis on self-improvement, weighted shifts, and linear dynamics. Our first main result shows that, for $1<p<\in…

math.FA2024★ 7 cited

On several dynamical properties of shifts acting on directed trees

Evgeny Abakumov, Arafat Abbar

This paper explores the notions of $F$ -transitivity and topological $F$ -recurrence for backward shift operators on weighted $ℓ^{p}$ -spaces and $c_{0}$ -spaces on…

math.FA2023

A note on the spectrum of Lipschitz operators and composition operators on Lipschitz spaces

Arafat Abbar, Clément Coine, Colin Petitjean

Fix a metric space $M$ and let $Lip_{0} (M)$ be the Banach space of complex-valued Lipschitz functions defined on $M$ . A weighted composition operator on $Lip_{0} (M)$ …

math.FA2023

A pre-adjoint approach on weighted composition operators between spaces of Lipschitz functions

Arafat Abbar, Clément Coine, Colin Petitjean

We consider weighted composition operators, that is operators of the type $g \mapsto w \cdot g \circ f$ , acting on spaces of Lipschitz functions. Bounded weighted composition opera…

math.FA2023

Orbits of the Backward Shifts with limit points

Evgeny Abakumov, Arafat Abbar

We show that the bilateral backward shift on $ℓ^{p} (Z, ω)$ that has a projective orbit with a non-zero limit point is supercyclic. This phenomenon holds also for $Γ$ -super…

math.FA2021

Compact and weakly compact Lipschitz operators

Arafat Abbar, Clément Coine, Colin Petitjean

Any Lipschitz map $f : M \to N$ between two pointed metric spaces may be extended in a unique way to a bounded linear operator $f : F (M) \to F (N)$ betwe…

math.FA2020

On the dynamics of Lipschitz operators

Arafat Abbar, Clément Coine, Colin Petitjean

By the linearization property of Lipschitz-free spaces, any Lipschitz map $f : M \to N$ between two pointed metric spaces may be extended uniquely to a bounded linear operator $\wi…

math.FA2020★ 4 cited

$Γ$ -supercyclicity of families of translates in weighted $L^{p}$ -spaces on locally compact groups

Arafat Abbar, Yulia Kuznetsova

Let $ω$ be a weight function defined on a locally compact group $G$ , $1 \leq p < + \infty$ , $S \subset G$ and let us assume that for any $s \in S$ , the left translation operator $T_{s}$ is…

On absolutely Cesàro bounded operators

On several dynamical properties of shifts acting on directed trees

A note on the spectrum of Lipschitz operators and composition operators on Lipschitz spaces

A pre-adjoint approach on weighted composition operators between spaces of Lipschitz functions

Orbits of the Backward Shifts with limit points

Compact and weakly compact Lipschitz operators

On the dynamics of Lipschitz operators

Γ-supercyclicity of families of translates in weighted Lp-spaces on locally compact groups

$Γ$ -supercyclicity of families of translates in weighted $L^{p}$ -spaces on locally compact groups