{
  "abstract": "Let $X$ be an infinite-dimensional complex Banach space and let $\\mathcal B(X)$ the full algebra of all bounded linear operator on $X$. In this paper, we give a complete characterization of surjective maps $ϕ:\\mathcal B(X)\\to\\mathcal B(X)$ satisfying \\[ r(AB)=0\\quad\\Longleftrightarrow\\quad r(ϕ(A)ϕ(B))=0 \\qquad(A,B\\in\\mathcal B(X)). \\] Without assuming additivity, injectivity, or continuity, we show that there exists a function $γ: B(X)\\mapsto \\C \\setminus\\{0\\}$ such that the map $ϕ$ takes one of the following forms: 1. there exists a bounded linear or conjugate-linear, invertible operator $S:X\\to X$ such that : \\label{eq:direct} ϕ(A)=γ(A)SAS^{-1},\\qquad \\text{ for all } \\quad A\\in B(X), 2. the space $X$ is reflexive and there exists a bounded linear or conjugate-linear, invertible operator $S:X^*\\to X$ such that \\label{eq:dual} ϕ(A)=γ(A)SA^*S^{-1},\\qquad \\text{ for all } \\quad A\\in B(X).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21840",
  "author_total": 2,
  "authors": [
    {
      "name": "Zakariae Azna"
    },
    {
      "name": "Fadil Chabbabi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d5jamdgk8zgtq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21840",
  "fulltext_url": null,
  "id": "d5jamdgk8zgtq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21840",
  "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",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7222521384",
  "pdf_url": "https://arxiv.org/pdf/2610.21840",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d5jamdgk8zgtq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21840",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21840"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Surjective maps preserving quasi-nilpotence of products of operators",
  "title_text": "Surjective maps preserving quasi-nilpotence of products of operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/d5jamdgk8zgtq",
  "venue": "arXiv",
  "versions": []
}