{
  "id": "math/0601645",
  "version": "v1",
  "published": "2006-01-26T16:21:07.000Z",
  "updated": "2006-01-26T16:21:07.000Z",
  "title": "$H^{\\infty}$ functional calculus and square functions on noncommutative $L^p$-spaces",
  "authors": [
    "Marius Junge",
    "Christian Le Merdy",
    "Quanhua Xu"
  ],
  "comment": "118 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this work we investigate semigroups of operators acting on noncommutative $L^p$-spaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and $H^\\infty$ functional calculus. We discuss several examples of noncommutative diffusion semigroups. This includes Schur multipliers, $q$-Ornstein-Uhlenbeck semigroups, and the noncommutative Poisson semigroup on free groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-01-26T16:21:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A60",
      "46L55",
      "46L69"
    ],
    "keywords": [
      "functional calculus",
      "free groups",
      "noncommutative square functions",
      "noncommutative diffusion semigroups",
      "schur multipliers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 118,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1645J"
    }
  }
}