{
  "abstract": "In this short note, we study the small perturbations of multiplication structure of a Banach algebra $\\mathcal A$, and its impact on the two Arens products on the bidual $\\mathcal A^{**}$. We show that the property of being \\say{Arens irregular} is stable under sufficiently small perturbation in the multiplication structure of a Banach algebra. Further we show that for any Banach function algebra which is equivalent to a uniform algebra, the Arens regularity is stable under small perturbation on the multiplication structure of the original Banach function algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11379",
  "author_total": 1,
  "authors": [
    {
      "name": "Deepika Rajoriya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8jy2c4dfk99k2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11379",
  "fulltext_url": null,
  "id": "8jy2c4dfk99k2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11379",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.11379",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8jy2c4dfk99k2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11379",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11379"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A note on the stability of Arens products under small perturbations of multiplication",
  "title_text": "A note on the stability of Arens products under small perturbations of multiplication",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/8jy2c4dfk99k2",
  "venue": "arXiv",
  "versions": []
}