{
  "abstract": "Let $ω: \\mathbb{N} \\to [1, \\infty)$ be a weight on the multiplicative semigroup of natural numbers. We investigate the Bochner-Schoenberg-Eberlein (BSE) property for the weighted Banach algebra of Dirichlet series $A_ω= \\ell^1(\\mathbb{N}, ω)$ under Dirichlet convolution. By employing Bohr's correspondence, we establish a weak-$\\ast$ approximation framework for $ω$-bounded semicharacters using scaled truncations that lie within the predual space $c_0(\\mathbb{N}, 1/ω)$. Utilizing the canonical $L$-projection decomposition of the bidual space $A_ω^{\\ast\\ast} = A_ω\\oplus c_0(\\mathbb{N}, 1/ω)^\\perp$ alongside the weak-$\\ast$ compactness of the unit ball via the Banach-Alaoglu theorem, we prove that $A_ω$ is a BSE-algebra for any weight. Furthermore, we show that the intrinsic BSE-norm on the Gel'fand transforms is isometric to the natural weighted algebra norm $\\|\\cdot\\|_ω$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15332",
  "author_total": 1,
  "authors": [
    {
      "name": "Prakash A. Dabhi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8hqbbg08mk579.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15332",
  "fulltext_url": null,
  "id": "8hqbbg08mk579",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15332",
  "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",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7213264624",
  "pdf_url": "https://arxiv.org/pdf/2609.15332",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8hqbbg08mk579.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15332",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15332"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The BSE Property for Weighted Banach Algebras of Dirichlet Series",
  "title_text": "The BSE Property for Weighted Banach Algebras of Dirichlet Series",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/8hqbbg08mk579",
  "venue": "arXiv",
  "versions": []
}