{
  "abstract": "We prove that every separable infinite-dimensional Fréchet algebra $X$ admits a continuous linear operator $T$ supporting a dense invariant hypercyclic algebra, giving an affirmative answer to a question of Bayart, Costa Jr. and Papathanasiou. In fact, every dense countable-dimensional subalgebra $\\mathcal A$ of $X$ can be prescribed as an invariant hypercyclic algebra. When $X$ admits a continuous norm, the operator can additionally be chosen in the form $T=I+K$, where $K$ is nuclear, so that $\\mathcal A = \\operatorname{span} \\operatorname{Orb}(a,T)$ for any prescribed $a\\in\\mathcal A\\backslash\\{0\\}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Bull. Braz. Math. Soc. (N.S.), volume 57(4), article number 43 (2026)",
  "arxiv": "2609.13983",
  "author_total": 2,
  "authors": [
    {
      "name": "Fernando Costa Jr."
    },
    {
      "name": "Álvaro Rocha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ez9q4zbvtgnc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13983",
  "fulltext_url": null,
  "id": "0ez9q4zbvtgnc",
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  "landing_url": "https://arxiv.org/abs/2609.13983",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
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  "pdf_url": "https://arxiv.org/pdf/2609.13983",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ez9q4zbvtgnc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2609.13983",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13983"
    }
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
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  ],
  "title": "Existence of hypercyclic algebras in Fréchet algebras",
  "title_text": "Existence of hypercyclic algebras in Fréchet algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/0ez9q4zbvtgnc",
  "venue": "arXiv",
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    {
      "doi": "10.1007/s00574-026-00534-2",
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}