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arXiv · 2609.02213

Invariant subspaces for free linearizations of Lipschitz maps

Clément Coine·Pedro L. Kaufmann·Colin Petitjean·Sebastián Tapia-García
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Abstract

We consider the invariant subspace problem for operators induced by Lipschitz self-maps on Lipschitz-free spaces. Besides the usual free linearizations $\widehat f$ of basepoint-preserving Lipschitz self-maps, we consider a wider class of operators $T_{f,e}$ which are naturally defined for arbitrary Lipschitz self-maps. We show, among other results, that every $\widehat f$ admits a non-trivial invariant subspace whenever the underlying metric space contains a compact ball, or has at least two connected components one of which has non-empty interior. We also obtain corresponding positive results for $T_{f,e}$ under isolated-point, compact-ball and disconnectedness assumptions, and discuss some consequences for linear dynamics.

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Clément Coine, Pedro L. Kaufmann, Colin Petitjean, Sebastián Tapia-García. 2026-09-02. Invariant subspaces for free linearizations of Lipschitz maps. https://arxiv.org/abs/2609.02213

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