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Article Dans Une Revue Integral Equations and Operator Theory Année : 2021

On the Dynamics of Lipschitz Operators

Résumé

By the linearization property of Lipschitz-free spaces, any Lipschitz map f : M → N between two pointed metric spaces may be extended uniquely to a bounded linear operator f : F (M) → F (N) between their corresponding Lipschitz-free spaces. In this note, we explore the connections between the dynamics of Lipschitz self-maps f : M → M and the linear dynamics of their extensions f : F (M) → F (M). This not only allows us to relate topological dynamical systems to linear dynamical systems but also provide a new class of hypercyclic operators acting on Lipschitz-free spaces.
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Dates et versions

hal-03025702 , version 1 (26-11-2020)

Identifiants

Citer

Arafat Abbar, Clément Coine, Colin Petitjean. On the Dynamics of Lipschitz Operators. Integral Equations and Operator Theory, 2021, ⟨10.1007/s00020-021-02662-4⟩. ⟨hal-03025702⟩
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