{
  "abstract": "Let $B(\\mathcal H)$ be the $*$-algebra of all bounded linear operators on a Hilbert space $\\mathcal H$. A classical result due to Stamplfi shows that, for any $a\\in B(\\mathcal H)$, the norm of the inner derivation $δ_a=[a,\\cdot]$ on $B(\\mathcal H)$ is given by $\\|δ_a\\|_{B(\\mathcal H)\\to B(\\mathcal H)}=2\\inf\\{ \\|a-c{\\bf 1}\\|_{B(\\mathcal H)}:c\\in \\mathbb{C}\\}$. In the present paper, we provide a formula for the norm of a generalized derivation implemented by self-adjoint operators from an ideal in $B(\\mathcal H)$, which partially answers a question posed by Fialkow and Loebl in the 1980s. We also consider this question in a more general setting of a symmetrically normed (not necessarily complete or separable) space affiliated with a properly infinite semifinite von Neumann algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Huang, J.; Pliev, M.; Sukochev, F.; Xu, R.; Norms of generalized derivations with values in symmetric spaces. Adv. Math. 495 (2026), Paper No. 110964, 25 pp",
  "arxiv": "2609.15233",
  "author_total": 4,
  "authors": [
    {
      "name": "J. Huang"
    },
    {
      "name": "M. Pliev"
    },
    {
      "name": "F. Sukochev"
    },
    {
      "name": "R. Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6r9srfzw6ta6z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15233",
  "fulltext_url": null,
  "id": "6r9srfzw6ta6z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15233",
  "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"
    ],
    [
      "arxiv",
      "math.OA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.15233",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6r9srfzw6ta6z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15233",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15233"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Norms of generalized derivations with values in symmetric spaces",
  "title_text": "Norms of generalized derivations with values in symmetric spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/6r9srfzw6ta6z",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1016/j.aim.2026.110964",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}