{
  "abstract": "Given $α\\in \\mathbb R$ and $ B_1,\\ldots,B_q\\in M_{m,n}$, consider the map \\[Φ^{\\pm}_{α,\\mathfrak{B}}(X)=α\\mbox{tr}(X) I_m\\pm \\sum_{s=1}^qB_sXB_s^*\\ \\mbox{for all}\\ X\\in M_n.\\] In this study, necessary and sufficient conditions on $α$ and $B_1,\\ldots,B_q$ are given that guarantee $Φ_{α,\\mathfrak{B}}^\\pm$ is $k$-positive, $k$-copositive, and $k$-PPT, respectively. As application, known results about the map $α\\mbox{tr}(X)I_n\\pm X$ are recovered. Furthermore, singular value inequalities associated with these positivity constraints are considered.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07260",
  "author_total": 3,
  "authors": [
    {
      "name": "Kennett L. Dela Rosa"
    },
    {
      "name": "Iana Angela C. Fajardo"
    },
    {
      "name": "Cedie B. Reyes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2f43pydf9vhjd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07260",
  "fulltext_url": null,
  "id": "2f43pydf9vhjd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07260",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7212051292",
  "pdf_url": "https://arxiv.org/pdf/2609.07260",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2f43pydf9vhjd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07260",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07260"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Family of Completely PPT Maps",
  "title_text": "A Family of Completely PPT Maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/2f43pydf9vhjd",
  "venue": "arXiv",
  "versions": []
}