8 papers
On absolutely Cesàro bounded operators
Arafat Abbar, Loris Arnold, Clément Coine
We study -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…
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 of basepoint-pr…
Higher order -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 . We establish that a function defined…
A note on the spectrum of Lipschitz operators and composition operators on Lipschitz spaces
Arafat Abbar, Clément Coine, Colin Petitjean
Fix a metric space and let be the Banach space of complex-valued Lipschitz functions defined on . A weighted composition operator on …
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 , acting on spaces of Lipschitz functions. Bounded weighted composition opera…
Growth rate of eventually positive Kreiss bounded -semigroups on and
L. Arnold, C. Coine
In this paper, we compare several Cesàro and Kreiss type boundedness conditions for a -semigroup on a Banach space and we show that those conditions are all equivalent for a p…
Compact and weakly compact Lipschitz operators
Arafat Abbar, Clément Coine, Colin Petitjean
Any Lipschitz map between two pointed metric spaces may be extended in a unique way to a bounded linear operator betwe…
On the dynamics of Lipschitz operators
Arafat Abbar, Clément Coine, Colin Petitjean
By the linearization property of Lipschitz-free spaces, any Lipschitz map between two pointed metric spaces may be extended uniquely to a bounded linear operator $\wi…