Clément Coine

activity

20202026

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.FA2026

Invariant subspaces for free linearizations of Lipschitz maps

Clément Coine, Pedro L. Kaufmann, Colin Petitjean +1

We consider the invariant subspace problem for operators induced by Lipschitz self-maps on Lipschitz-free spaces. Besides the usual free linearizations $f$ of basepoint-pr…

math.FA2024

Higher order $S^{p}$ -differentiability: The unitary case

Arup Chattopadhyay, Clément Coine, Saikat Giri +1

Consider the set of unitary operators on a complex separable Hilbert space $\hilh$, denoted as $\mathcal{U}(\hilh)$. Consider $1 < p < \infty$ . We establish that a function $f$ defined…

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.FA2022

Growth rate of eventually positive Kreiss bounded $C_{0}$ -semigroups on $L^{p}$ and $C (K)$

L. Arnold, C. Coine

In this paper, we compare several Cesàro and Kreiss type boundedness conditions for a $C_{0}$ -semigroup on a Banach space and we show that those conditions are all equivalent for a p…

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…

On absolutely Cesàro bounded operators

Invariant subspaces for free linearizations of Lipschitz maps

Higher order Sp-differentiability: The unitary case

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

Growth rate of eventually positive Kreiss bounded C0​-semigroups on Lp and C(K)

Compact and weakly compact Lipschitz operators

On the dynamics of Lipschitz operators

Higher order $S^{p}$ -differentiability: The unitary case

Growth rate of eventually positive Kreiss bounded $C_{0}$ -semigroups on $L^{p}$ and $C (K)$