{
  "abstract": "We prove that, for real Banach spaces of dimension greater than one, each of the identities $\\|Id+T^2\\|=1+\\|T^2\\|$ and $\\|Id-T^2\\|=1+\\|T^2\\|$, required for every rank-one operator $T$, characterizes the Daugavet property, thereby answering a question posed by Kadets, Martín, and Merí (2007). Consequently, every extremely non-complex Banach space of dimension greater than one has the Daugavet property, answering a question of Martín and Merí (2011). We also compare pointwise versions of the square Daugavet properties with Daugavet points, $Δ$-points, and $\\nabla$-points.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27693",
  "author_total": 1,
  "authors": [
    {
      "name": "Johann Langemets"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0e3kan68fvwgn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27693",
  "fulltext_url": null,
  "id": "0e3kan68fvwgn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27693",
  "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": "W7214166380",
  "pdf_url": "https://arxiv.org/pdf/2609.27693",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0e3kan68fvwgn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27693",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27693"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Characterizing the Daugavet property by squares of rank-one operators",
  "title_text": "Characterizing the Daugavet property by squares of rank-one operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/0e3kan68fvwgn",
  "venue": "arXiv",
  "versions": []
}