{
  "abstract": "Let $ G $ be a compact metrizable Abelian group, $ L^{1}(G) $ its group algebra and $ M(G) $ its measure algebra. For each proper subset $ E $ of the dual group $ \\hat{G} $, let $ L^{1}_{E}(G)=\\{f\\in L^{1}(G):\\hat{f}=0 \\text{ on } \\hat{G}\\setminus E \\}$ and $M_{E}=\\{μ\\in M(G):\\hatμ=0 \\text{ on }\\hat{G}\\setminus E\\} $. If $ M_{E}(G)=L^{1}_{E}(G) $ then the set $ E $ is said to be a Riesz sets. If $ M_{E}(G)*M_{E}(G)\\subseteq L_{E}^{1}(G) $ then $ E $ is said to be a small-2 set. The main results of this paper are the following: 1. Every small-2 set is a Riesz set. 2. The ideal $ L^{1}_{E}(G) $ is Arens regular iff $ E $ is a Riesz set. Let $ A=L_{E}(G) $ and equip $ A^{**} $ with the first Arens product. 3. The centre of $ A^{**} $ is $ Z(A^{**})=A+N(A^{**}) $, where $ N(A^{**})=\\{r\\in A^{**}:rA^{**}=\\{0\\}\\} $. These results settle three long-standing open problems in this area.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.30570",
  "author_total": 2,
  "authors": [
    {
      "name": "A. To-Ming Lau"
    },
    {
      "name": "A. Ülger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c8n9xztt1gyqv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.30570",
  "fulltext_url": null,
  "id": "c8n9xztt1gyqv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.30570",
  "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": "W7166742526",
  "pdf_url": "https://arxiv.org/pdf/2606.30570",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c8n9xztt1gyqv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2606.30570",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.30570"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Small-2 Sets Are Riesz Sets",
  "title_text": "Small-2 Sets Are Riesz Sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/c8n9xztt1gyqv",
  "venue": "arXiv",
  "versions": []
}