{
  "abstract": "We study the spaces of bounded multilinear operators $\\mathcal L^i(X,Y)$ endowed with $L^p_μ$-norms, where $X,Y$ are normed spaces and $μ$ is a measure with $p$-moments. These are norms without taking a quotient, under suitable support conditions. The topology induced coincides with the strong operator and compact-open topologies on operator-norm-bounded subsets. Furthermore, we identify the completion of these spaces with spaces of Hilbert--Schmidt operators on the reproducing kernel Hilbert space (RKHS) for $p=2$; with iterated $γ$-radonifying multilinear operators on the RKHS in the Gaussian case, for general $p$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19151",
  "author_total": 1,
  "authors": [
    {
      "name": "Filippo de Feo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dcsw8cpw6tbxr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19151",
  "fulltext_url": null,
  "id": "dcsw8cpw6tbxr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19151",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7222291352",
  "pdf_url": "https://arxiv.org/pdf/2610.19151",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dcsw8cpw6tbxr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19151",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19151"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "$L^p_μ$-Normed Spaces of Bounded Multilinear Operator",
  "title_text": "L^p_μ-Normed Spaces of Bounded Multilinear Operator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/dcsw8cpw6tbxr",
  "venue": "arXiv",
  "versions": []
}