{
  "id": "1802.06227",
  "version": "v1",
  "published": "2018-02-17T11:55:47.000Z",
  "updated": "2018-02-17T11:55:47.000Z",
  "title": "On some geometric properties of operator spaces",
  "authors": [
    "Arpita Mal",
    "Debmalya Sain",
    "Kallol Paul"
  ],
  "comment": "18 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper we study some geometric properties like parallelism, orthogonality and semi-rotundity in the space of bounded linear operators. We completely characterize parallelism of two compact linear operators between normed linear spaces $\\mathbb{X} $ and $\\mathbb{Y}$, assuming $\\mathbb{X}$ to be reflexive. We also characterize parallelism of two bounded linear operators between normed linear spaces $\\mathbb{X} $ and $\\mathbb{Y}.$ We investigate parallelism and approximate parallelism in the space of bounded linear operators defined on a Hilbert space. Using the characterization of operator parallelism, we study Birkhoff-James orthogonality in the space of compact linear operators as well as bounded linear operators. Finally, we introduce the concept of semi-rotund points (semi-rotund spaces) which generalizes the notion of exposed points (strictly convex spaces). We further study semi-rotund operators and prove that $\\mathbb{B}(\\mathbb{X},\\mathbb{Y})$ is a semi-rotund space which is not strictly convex, if $\\mathbb{X},\\mathbb{Y}$ are finite-dimensional Banach spaces and $\\mathbb{Y}$ is strictly convex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-17T11:55:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "47L05"
    ],
    "keywords": [
      "bounded linear operators",
      "geometric properties",
      "operator spaces",
      "compact linear operators",
      "normed linear spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}