{
  "id": "1907.08620",
  "version": "v1",
  "published": "2019-07-19T09:53:10.000Z",
  "updated": "2019-07-19T09:53:10.000Z",
  "title": "Bishop-Phelps-Bollobás property for positive operators when the domain is $L_\\infty $",
  "authors": [
    "M. D. Acosta",
    "M. Soleimani-Mourchehkhorti"
  ],
  "comment": "18 pages. arXiv admin note: text overlap with arXiv:1905.12972",
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that the class of positive operators from $L_\\infty (\\mu)$ to $Y$ has the Bishop-Phelps-Bollob\\'as property for any positive measure $\\mu$, whenever $Y$ is a uniformly monotone Banach lattice with a weak unit. The same result also holds for the pair $(c_0, Y)$ for any uniformly monotone Banach lattice $Y.$ Further we show that these results are optimal in case that $Y$ is strictly monotone.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-19T09:53:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B04",
      "47B99"
    ],
    "keywords": [
      "positive operators",
      "bishop-phelps-bollobás property",
      "uniformly monotone banach lattice",
      "weak unit",
      "bishop-phelps-bollobas property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}