{
  "abstract": "We study Schatten embeddings through circular means of trace powers. In finite dimensions, a decomposition by singular-value vanishing orders shows that every term of order at most two has a nonnegative coefficient. This yields the classification $\\ell_q^2(\\C)\\hookrightarrow\\Sp_p^n$ if and only if $q=p$ or $q=2$, for $n\\ge2$ and $p<\\infty$. In particular, it gives negative answers to parts (ii), (iii), and (iv) of Problem 3.1 in Chattopadhyay--Pradhan--Skripka, arXiv:2603.07359v2. A regularized curvature estimate also excludes $\\ell_q^2$ from infinite-dimensional $\\Sp_p$ for $0<p\\le2<q\\le\\infty$ and gives finite-rank distortion bounds. The other parts of that problem are not claimed to be solved.Our results extend previous studies on Schatten embeddings, particularly those in \\cite{CHPPR, CHPR, CPS}, by developing a complex-curvature framework based on complex convexity theories \\cite{BR,DGT}, which resolves several remaining quasi-Banach cases and yields new geometric obstructions for isometric embeddings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37504",
  "author_total": 3,
  "authors": [
    {
      "name": "Ying Xu"
    },
    {
      "name": "Wenwen Zhang"
    },
    {
      "name": "Qi Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4mfjv0shjj4pn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37504",
  "fulltext_url": null,
  "id": "4mfjv0shjj4pn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37504",
  "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/2609.37504",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4mfjv0shjj4pn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37504",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37504"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Further Results on the Isometric Embeddability of \\(S_q^m\\) into \\(S_p^n\\)",
  "title_text": "Further Results on the Isometric Embeddability of S_q^m into S_p^n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/4mfjv0shjj4pn",
  "venue": "arXiv",
  "versions": []
}