{
  "id": "1309.4974",
  "version": "v1",
  "published": "2013-09-19T13:42:48.000Z",
  "updated": "2013-09-19T13:42:48.000Z",
  "title": "Multiplication operators on $L_p$ spaces and homological triviality of respective category of modules",
  "authors": [
    "Norbert Nemesh"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We give complete characterisation of topologically injective (bounded below), topologically surjective (open mapping), isometric and coisometric (quotient mapping) multiplication operators between $L_p$ spaces defined on different $\\sigma$-finite measure spaces. We prove that all such operators invertible from the left or from the right. As the consequence we prove that all objects of the category of $L_p$ spaces considered as left Banach modules over algebra of bounded measurable functions are metrically, extremelly and relatively projective, injective and flat.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-19T13:42:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30",
      "46M10"
    ],
    "keywords": [
      "multiplication operators",
      "homological triviality",
      "respective category",
      "finite measure spaces",
      "left banach modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.4974N"
    }
  }
}