{
  "abstract": "We construct an explicit symmetric Banach norm on a function space over $(0,\\infty)$ which is monotone with respect to logarithmic submajorization but is not strongly symmetric, and hence is not fully symmetric. This answers a question raised by Dodds, Dodds, Sukochev, and Zanin. We also construct a strongly symmetric Banach function space over $(0,\\infty)$ which is monotone with respect to logarithmic submajorization and admits no equivalent fully symmetric norm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20270",
  "author_total": 1,
  "authors": [
    {
      "name": "Jinghao Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/60nacfdph7rj6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20270",
  "fulltext_url": null,
  "id": "60nacfdph7rj6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20270",
  "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": "W7213612353",
  "pdf_url": "https://arxiv.org/pdf/2609.20270",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/60nacfdph7rj6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20270",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20270"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A logarithmically monotone symmetric norm which is not fully symmetric",
  "title_text": "A logarithmically monotone symmetric norm which is not fully symmetric",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/60nacfdph7rj6",
  "venue": "arXiv",
  "versions": []
}