{
  "abstract": "We study Tauberian conditions on the successive differences of real sequences which ensure that: (i) ordinary convergence coincides with ideal convergence; or (ii) every ordinary accumulation point is an ideal cluster point; or (iii) every ordinary accumulation point is an ideal limit point. First, we prove that an ideal $\\mathcal{I}$ has the Baire property if and only if there exists a positive sequence $(r_n)$ tending to zero, with $\\sum_n r_n=\\infty$, such that $$ |x_{n+1}-x_n|=O(r_n) $$ is a Tauberian condition for any of the three previous statements. Second, for analytic $P$-ideals, we characterize the validity of the Tauberian rate $O(1/n)$ in terms of properties of lower semicontinuous submeasures which represent it. Lastly, in the case of statistical limit points, we prove that $o(1/n)$ is a Tauberian condition for the statement (iii), whereas $O(1/n)$ need not suffice: in this sense, $o(1/n)$ is an optimal Tauberian rate for (iii). On the other hand, for statistical cluster points in (ii), $O(1/n)$ is an optimal one among nonincreasing rates. For every positive null sequence $(r_n)$ with divergent sum, we also construct a summable ideal $\\mathcal{I}$ for which $o(r_n)$ is an optimal Tauberian rate for both statements (ii) and (iii).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21889",
  "author_total": 1,
  "authors": [
    {
      "name": "Paolo Leonetti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7j4q7sb3yx64g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21889",
  "fulltext_url": null,
  "id": "7j4q7sb3yx64g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21889",
  "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.CA"
    ],
    [
      "openalex",
      "2613|Approximation Theory and Sequence Spaces"
    ]
  ],
  "openalex": "W7222498269",
  "pdf_url": "https://arxiv.org/pdf/2610.21889",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7j4q7sb3yx64g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21889",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21889"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Tauberian rates and the Baire property of ideals",
  "title_text": "Tauberian rates and the Baire property of ideals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/7j4q7sb3yx64g",
  "venue": "arXiv",
  "versions": []
}