{
  "abstract": "It is shown that a bounded linear map on a complex separable Hilbert space with non-trivial invariant probability measures doesn't have to possess eigenvalues. This resolves a question indicated by Flytzanis in 1995 and concretely asked by Grivaux--López-Martínez from 2023 resp. Grivaux--Matheron--Menet from 2021. Still, as a positive result, we prove that every bounded linear operator on a separable complex Banach space for which a non-fixing invariant probability measure exists, has to have some approximate point spectrum on the unit circle minus $1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05735",
  "author_total": 1,
  "authors": [
    {
      "name": "Yannic Steenbeck"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4nzprhfx37np0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05735",
  "fulltext_url": null,
  "id": "4nzprhfx37np0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05735",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7212020190",
  "pdf_url": "https://arxiv.org/pdf/2609.05735",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4nzprhfx37np0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05735",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05735"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Can one feel the existence of a non-trivial invariant measure?",
  "title_text": "Can one feel the existence of a non-trivial invariant measure?",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/4nzprhfx37np0",
  "venue": "arXiv",
  "versions": []
}