{
  "abstract": "We construct equivalent norms on $L_1[0,1]$, arbitrarily close to the usual $L_1$-norm, which are weakly midpoint locally uniformly rotund and Gâteaux smooth, and whose dual norms have the Daugavet property. In particular, we obtain a strictly convex and smooth Banach space with the Daugavet property, thereby solving a longstanding open problem in the area.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12562",
  "author_total": 3,
  "authors": [
    {
      "name": "Sheldon Dantas"
    },
    {
      "name": "Jaan Kristjan Kaasik"
    },
    {
      "name": "Yoël Perreau"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/46qye7awh3pvg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12562",
  "fulltext_url": null,
  "id": "46qye7awh3pvg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12562",
  "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.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7213117229",
  "pdf_url": "https://arxiv.org/pdf/2609.12562",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/46qye7awh3pvg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12562",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12562"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A strictly convex and smooth Banach space with the Daugavet property",
  "title_text": "A strictly convex and smooth Banach space with the Daugavet property",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/46qye7awh3pvg",
  "venue": "arXiv",
  "versions": []
}