{
  "abstract": "Kramar and Kramar Fijavž proved that a commutator $Y=AB-BA$ of two complex square matrices is nilpotent whenever $Y$ commutes with an iterated commutator $δ_Y^{k}(A)$, where $δ_Y(T)=YT-TY$, and asked whether this result can be generalized to bounded operators on infinite-dimensional spaces. We show that for $k\\geq 2$ such a commutator need not be quasinilpotent. On the other hand, for every $k$ it is quasinilpotent whenever it is compact, or more generally whenever it is a Riesz operator or $AY-YA$ is compact. Moreover, its Riesz projection at any non-zero isolated point of its spectrum always has infinite rank.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06423",
  "author_total": 1,
  "authors": [
    {
      "name": "Hranislav Stanković"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2qa476nn4sv3s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06423",
  "fulltext_url": null,
  "id": "2qa476nn4sv3s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06423",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06423",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2qa476nn4sv3s.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06423",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06423"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Quasinilpotency of commutators under a weakened Kleinecke--Shirokov condition",
  "title_text": "Quasinilpotency of commutators under a weakened Kleinecke--Shirokov condition",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/2qa476nn4sv3s",
  "venue": "arXiv",
  "versions": []
}