{
  "id": "math/0010155",
  "version": "v1",
  "published": "2000-10-15T22:00:35.000Z",
  "updated": "2000-10-15T22:00:35.000Z",
  "title": "The $H^{\\infty}-$calculus and sums of closed operators",
  "authors": [
    "N. J. Kalton",
    "L. Weis"
  ],
  "comment": "26 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We develop a very general operator-valued functional calculus for operators with an $H^{\\infty}-$calculus. We then apply this to the joint functional calculus of two commuting sectorial operators when one has an $H^{\\infty}$calculus. Using this we prove theorem of Dore-Venni type on sums of commuting sectorial operators and apply our results to the problem of $L_p-$maximal regularity. Our main assumption is the R-boundedness of certain sets of operators, and therefore methods from the geometry of Banach spaces are essential here. In the final section we exploit the special Banach space structure of $L_1-$spaces and $C(K)-$spaces, to obtain some more detailed results in this setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-10-15T22:00:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A60",
      "47D06"
    ],
    "keywords": [
      "closed operators",
      "commuting sectorial operators",
      "special banach space structure",
      "joint functional calculus",
      "general operator-valued functional calculus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.....10155K"
    }
  }
}