{
  "abstract": "We solve a problem posed by Audenaert and Kittaneh in 2012 by proving that the Aujla--Bourin subadditivity inequality can be strengthened to an optimal form. We also answer questions posed by Bourin and the second author: (1) we significantly extend both the reciprocal Lie--Trotter theorem of Audenaert and Hiai and Kato's limit theorem; (2) we determine the best constants in inequalities for sums of contractions and positive block matrices, including the sharp triangle inequality $$ |A+B+C| \\leq \\frac{3}{4} I + |A|+|B|+|C| $$ for three contractions $A,B,C$; and (3) we prove a remarkable eigenvalue inequality for the symmetric modulus, thereby determining the best dimension-free lower bound in a question studied by Bourin, Lee, and Zhang.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20094",
  "author_total": 2,
  "authors": [
    {
      "name": "Mohamed Amine Aouichaoui"
    },
    {
      "name": "Eun-Young Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ah8avrzva3qtq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20094",
  "fulltext_url": null,
  "id": "ah8avrzva3qtq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20094",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.20094",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ah8avrzva3qtq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.20094",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20094"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Solutions to some open problems in matrix analysis",
  "title_text": "Solutions to some open problems in matrix analysis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/ah8avrzva3qtq",
  "venue": "arXiv",
  "versions": []
}