{
  "abstract": "We investigate the typical dynamical properties of hypercyclic operators in $\\mathcal{L}_M(X)$, the set of all bounded linear operators on $X$ whose norms are at most $M$, when $X=\\ell_p$, $1< p<\\infty$. We show that, with respect to SOT$^*$, a typical operator $T\\in \\mathcal{L}_M(X)$ is weakly mixing, is weakly disjoint from a given hypercyclic operator $S$, is not topologically ergodic, and satisfies $(T,T^2,\\dotsc,T^k)$ is disjoint hypercyclic for any $k\\geq 2$. We also show that the similar typical dynamical properties for the concrete family $\\mathcal{M}=\\{I+B_w\\in \\mathcal{L}(X)\\colon w\\in c_0(\\mathbb{Z})\\}$, endowed with the norm topology, where $B_w$ is a bilateral weighted backward shift.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10957",
  "author_total": 2,
  "authors": [
    {
      "name": "Jian Li"
    },
    {
      "name": "Qijing Liao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f09erv4ca0fq9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10957",
  "fulltext_url": null,
  "id": "f09erv4ca0fq9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10957",
  "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": "W7212286258",
  "pdf_url": "https://arxiv.org/pdf/2609.10957",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f09erv4ca0fq9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.10957",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10957"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Typical dynamical properties of operators on $\\ell_p$",
  "title_text": "Typical dynamical properties of operators on ℓ_p",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/f09erv4ca0fq9",
  "venue": "arXiv",
  "versions": []
}