{
  "id": "2209.05397",
  "version": "v1",
  "published": "2022-09-08T10:06:00.000Z",
  "updated": "2022-09-08T10:06:00.000Z",
  "title": "Non-linear traces on the algebra of compact operators and majorization",
  "authors": [
    "Masaru Nagisa",
    "Yasuo Watatani"
  ],
  "comment": "32 pages, 3figures. arXiv admin note: substantial text overlap with arXiv:2109.02031",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "We study non-linear traces of Choquet type and Sugeno type on the algebra of compact operators. They have certain partial additivities. We show that these partial additivities characterize non-linear traces of both Choquet type and Sugeno type respectively. There exists a close relation between non-linear traces of Choquet type and majorization theory. We study trace class operators for non-linear traces of Choquet type. More generally we discuss Schatten-von Neumann $p$-class operators for non-linear traces of Choquet type. We determine when they form Banach spaces. This is an attempt of non-commutative integration theory for non-linear traces of Choquet type on the algebra of compact operators. We also consider the triangle inequality for non-linear traces of Sugeno type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-08T10:06:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L51",
      "47B06",
      "47B10"
    ],
    "keywords": [
      "compact operators",
      "choquet type",
      "sugeno type",
      "majorization",
      "partial additivities characterize non-linear traces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}