{
  "id": "1812.00167",
  "version": "v1",
  "published": "2018-12-01T07:36:34.000Z",
  "updated": "2018-12-01T07:36:34.000Z",
  "title": "The operator--valued parallelism and norm-parallelism in matrices",
  "authors": [
    "M. Mohammadi Gohari",
    "M. Amyari"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\mathcal{H}$ be a Hilbert space, and let $K(\\mathcal{H})$ be the $C^*$-algebra of compact operators on $\\mathcal{H}$. In this paper, we present some characterizations of the norm-parallelism for elements of a Hilbert $K(\\mathcal{H})$-module by employing the Birkhoff--James orthogonality. Among other things, we present a characterization of transitive relation of the norm-parallelism for elements in a certain Hilbert $K(\\mathcal{H})$-module. We also give some characterizations of the Schatten $p$-norms and the operator norm-parallelism for matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-01T07:36:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L08",
      "47A30",
      "47B10",
      "47B47"
    ],
    "keywords": [
      "operator-valued parallelism",
      "characterization",
      "operator norm-parallelism",
      "birkhoff-james orthogonality",
      "compact operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}