{
  "abstract": "In this paper we will investigate Pettis integrability of $\\mathcal{C}^{\\circ}_Φ(\\mathcal{H})$-valued functions. We will study weakly$^*$ integrable $\\mathcal{B}(\\mathcal{H})$-valued functions and establish sufficient conditions for such functions to be Pettis integrable as $\\mathcal{C}^{\\circ}_Φ(\\mathcal{H})$-valued functions. In addition, we prove the inequality $$\\left\\|\\int_E\\mathscr{A}^*\\mathscr{B}dμ\\right\\|_{Φ^{(p)}} \\leqslant \\|\\mathscr{A}\\|_{L^q_s}\\cdot\\left\\|\\sqrt[p]{\\int_E|\\mathscr{B}|^pdμ}\\right\\|_{Φ^{(p)}},$$ where $Φ^{(p)}$ is $p$-modification of the function $Φ$ and the functions $\\mathscr{A}$ and $\\mathscr{B}$ belong to the suitable spaces of operator-valued functions. Finally, under some additional integrability assumptions on $\\mathscr{B}$ we provide similar estimates of the Pettis norm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.02790",
  "author_total": 3,
  "authors": [
    {
      "name": "Mihailo Krstić"
    },
    {
      "name": "Matija Milović"
    },
    {
      "name": "Stefan Milošević"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fn9ezaxwxr5ex.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.02790",
  "fulltext_url": null,
  "id": "fn9ezaxwxr5ex",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.02790",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7167593706",
  "pdf_url": "https://arxiv.org/pdf/2607.02790",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fn9ezaxwxr5ex.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2607.02790",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.02790"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Pettis integrability of functions with values in separable symmetrically-normed ideals and related norm estimates",
  "title_text": "Pettis integrability of functions with values in separable symmetrically-normed ideals and related norm estimates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/fn9ezaxwxr5ex",
  "venue": "arXiv",
  "versions": []
}