{
  "id": "1807.03780",
  "version": "v1",
  "published": "2018-07-10T09:39:56.000Z",
  "updated": "2018-07-10T09:39:56.000Z",
  "title": "Characterizations of norm--parallelism in spaces of continuous functions",
  "authors": [
    "Ali Zamani"
  ],
  "comment": "to appear in Bulletin of the Iranian Mathematical Society",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we consider the characterization of norm--parallelism problem in some classical Banach spaces. In particular, for two continuous functions $f, g$ on a compact Hausdorff space $K$, we show that $f$ is norm--parallel to $g$ if and only if there exists a probability measure (i.e. positive and of full measure equal to $1$) $\\mu$ with its support contained in the norm attaining set $\\{x\\in K: \\, |f(x)| = \\|f\\|\\}$ such that $\\big|\\int_K \\overline{f(x)}g(x)d\\mu(x)\\big| = \\|f\\|\\,\\|g\\|$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-10T09:39:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A30",
      "46B20",
      "46E15"
    ],
    "keywords": [
      "continuous functions",
      "characterization",
      "full measure equal",
      "compact hausdorff space",
      "norm attaining set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}