{
  "abstract": "Let $E$ and $F$ be separable symmetric Banach sequence spaces, and let $C_E$ and $C_F$ be the corresponding ideals of compact operators on a separable Hilbert space. We prove that if $C_F$ is isomorphic to a complemented subspace of $S_E$, then $F=\\ell_2$. As a consequence, if $C_E$ is isomorphic to $C_F$, then $E=F$ with equivalent norms. This answers Pełczyński's 1979 question concerning the uniqueness of symmetric structure. We also strengthen Arazy's result by showing that if $E$ has finite cotype and $C_F$ embeds isomorphically into $S_E$, then $F=\\ell_2$. For reflexive $F\\ne\\ell_2$ with non-trivial Boyd indices, the embedding theorems of Lindenstrauss and Szankowski yield a separable reflexive symmetric sequence space $E$ with trivial cotype such that $C_F$ embeds isomorphically into $S_E$. This gives negative answers to several questions raised by Arazy in 1981.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09923",
  "author_total": 2,
  "authors": [
    {
      "name": "Tianbao Guo"
    },
    {
      "name": "Jinghao Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1e6gra4f9ync5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09923",
  "fulltext_url": null,
  "id": "1e6gra4f9ync5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09923",
  "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": "W7221032589",
  "pdf_url": "https://arxiv.org/pdf/2610.09923",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1e6gra4f9ync5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09923",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09923"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On Pełczyński's problem concerning the uniqueness of symmetric structure",
  "title_text": "On Pełczyński's problem concerning the uniqueness of symmetric structure",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/1e6gra4f9ync5",
  "venue": "arXiv",
  "versions": []
}