{
  "abstract": "We study the Almost-Invariant Subspace Problem for operators defined on non-normable Fréchet spaces and especially on $ω$. This problem is stated as follows: \"Given a bounded operator $T$ on an infinite-dimensional complex Fréchet space $X$, can we always find a closed almost-invariant half-space?\". In this paper we solve the problem for the space $ω$ by showing that an operator $T$ on $ω$ possesses a closed almost-invariant half-space if and only if $T$ is conjugate to $F + R + λ\\operatorname{Id}$ or to $B + R + λ\\operatorname{Id}$ where $F$ is the Forward shift and $B$ is the Backward shift and where $R$ is a finite rank operator and $λ\\in \\mathbb{C}$. We also investigate the case of operators defined on $X \\oplus ω$ where $X$ is an infinite-dimensional Fréchet space with a continuous norm and we show that in this case, every operator defined on $X \\oplus ω$ possesses a closed almost-invariant half-space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03468",
  "author_total": 1,
  "authors": [
    {
      "name": "Noémie Fougnies"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2kgmvpxfcq25x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03468",
  "fulltext_url": null,
  "id": "2kgmvpxfcq25x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03468",
  "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",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7208740356",
  "pdf_url": "https://arxiv.org/pdf/2609.03468",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2kgmvpxfcq25x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03468",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03468"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Almost-invariant half-spaces of operators on $ω$",
  "title_text": "Almost-invariant half-spaces of operators on ω",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/2kgmvpxfcq25x",
  "venue": "arXiv",
  "versions": []
}