{
  "id": "1208.4912",
  "version": "v1",
  "published": "2012-08-24T06:59:40.000Z",
  "updated": "2012-08-24T06:59:40.000Z",
  "title": "Characterizations of Connections for Positive Operators",
  "authors": [
    "Pattrawut Chansangiam",
    "Wicharn Lewkeeratiyutkul"
  ],
  "comment": "12 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "An axiomatic theory of operator connections and operator means was investigated by Kubo and Ando in 1980. A connection is a binary operation for positive operators satisfying the monotonicity, the transformer inequality and the joint-continuity from above. In this paper, we show that the joint-continuity assumption can be relaxed to some conditions which are weaker than the separate-continuity. This provides an easier way for checking whether a given binary opertion is a connection. Various axiomatic characterizations of connections are obtained. We show that the concavity is an important property of a connection by showing that the monotonicity can be replaced by the concavity or the midpoint concavity. Each operator connection induces a unique scalar connection. Moreover, there is an affine order isomorphism between connections and induced connections. This gives a natural viewpoint to define any named means.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-24T06:59:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A63",
      "47A64"
    ],
    "keywords": [
      "positive operators",
      "characterizations",
      "affine order isomorphism",
      "unique scalar connection",
      "operator connection induces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.4912C"
    }
  }
}