{
  "abstract": "Let $\\mathcal{F}_T$ be the analytic functional system generated by a linear bounded operator $T$ on an infinite dimensional complex Hilbert space. This paper characterizes the stability of property (R), a variant of Weyl's theorem, for $\\mathcal{F}_T$ and under compact perturbations in terms of the spectrum on consistency in Weyl. In particular, the stability of property (R) under compact perturbations is shown to imply the (R)-stability of $\\mathcal{F}_T$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29710",
  "author_total": 3,
  "authors": [
    {
      "name": "Sinan Qiu"
    },
    {
      "name": "Lining Jiang"
    },
    {
      "name": "Xiaomin Wei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cy09b7km2zsgx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29710",
  "fulltext_url": null,
  "id": "cy09b7km2zsgx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29710",
  "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.SP"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7223203349",
  "pdf_url": "https://arxiv.org/pdf/2610.29710",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cy09b7km2zsgx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29710",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29710"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Property (R) with its stability for analytic functional system and under compact perturbations",
  "title_text": "Property (R) with its stability for analytic functional system and under compact perturbations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/cy09b7km2zsgx",
  "venue": "arXiv",
  "versions": []
}