{
  "id": "2006.06440",
  "version": "v1",
  "published": "2020-06-11T13:52:38.000Z",
  "updated": "2020-06-11T13:52:38.000Z",
  "title": "Some remarks on orthogonality of bounded linear operators",
  "authors": [
    "Anubhab Ray",
    "Debmalya Sain",
    "Subhrajit Dey",
    "Kallol Paul"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We explore the relation between the orthogonality of bounded linear operators in the space of operators and that of elements in the ground space. To be precise, we study if $ T, A \\in \\mathbb{L}(\\mathbb{X}, \\mathbb{Y}) $ satisfy $ T \\bot_B A,$ then whether there exists $ x \\in \\mathbb{X} $ such that $ Tx\\bot_B Ax$ with $ \\|x\\| =1, \\|Tx\\| = \\|T\\|$, where $\\mathbb{X}, \\mathbb{Y} $ are normed linear spaces. In this context, we introduce the notion of Property $ P_n $ for a Banach space and illustrate its connection with orthogonality of a bounded linear operator between Banach spaces. We further study Property $ P_n $ for various polyhedral Banach spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-11T13:52:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "47L05"
    ],
    "keywords": [
      "bounded linear operator",
      "orthogonality",
      "polyhedral banach spaces",
      "normed linear spaces",
      "ground space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}