{
  "abstract": "Given $0<r_{j}<1$ with $r_{j}\\to1$, there exist a normal operator $T$ on $\\ell^{2}$ with eigenvalues $λ_{j}$ satisfying $|λ_{j}|=r_{j}$ and $g\\in\\ell^{2}$ such that \\[ \\left\\{ \\frac{T^{n}g}{\\left\\Vert T^{n}g\\right\\Vert }\\right\\} _{n\\geq0}\\text{is a frame}\\:\\Longleftrightarrow\\:\\sum_{j\\geq1}\\left(1-r^{2}_{j}\\right)=\\infty. \\] Whenever this condition holds, the frame bounds can be chosen with ratio arbitrarily close to one.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19545",
  "author_total": 1,
  "authors": [
    {
      "name": "James Tian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f324hwpfjyy9w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19545",
  "fulltext_url": null,
  "id": "f324hwpfjyy9w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19545",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
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      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
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  ],
  "openalex": "W7221985911",
  "pdf_url": "https://arxiv.org/pdf/2610.19545",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f324hwpfjyy9w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19545",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19545"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Normalized Orbit Frames and Essential Spectrum, II",
  "title_text": "Normalized Orbit Frames and Essential Spectrum, II",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/f324hwpfjyy9w",
  "venue": "arXiv",
  "versions": []
}