{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02213",
  "author_total": 4,
  "authors": [
    {
      "name": "Clément Coine"
    },
    {
      "name": "Pedro L. Kaufmann"
    },
    {
      "name": "Colin Petitjean"
    },
    {
      "name": "Sebastián Tapia-García"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eb3ekv0ptgjn3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02213",
  "fulltext_url": null,
  "id": "eb3ekv0ptgjn3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02213",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7208794448",
  "pdf_url": "https://arxiv.org/pdf/2609.02213",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eb3ekv0ptgjn3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2609.02213",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02213"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Invariant subspaces for free linearizations of Lipschitz maps",
  "title_text": "Invariant subspaces for free linearizations of Lipschitz maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/eb3ekv0ptgjn3",
  "venue": "arXiv",
  "versions": []
}