{
  "id": "1004.1529",
  "version": "v2",
  "published": "2010-04-09T11:11:48.000Z",
  "updated": "2010-08-06T09:41:33.000Z",
  "title": "Positivstellensätze for Algebras of Matrices",
  "authors": [
    "Yurii Savchuk",
    "Konrad Schmüdgen"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AG",
    "math.OA",
    "math.RA"
  ],
  "abstract": "The paper is concerned with various types of noncommutative Positivstellens\\\"atze for the matrix algebra $M_n(\\cA)$, where $\\cA$ is an algebra of operators acting on a unitary space, a path algebra, a cyclic algebra or a formally real field. Some new types of Positivstellens\\\"atze are proposed and proved, it is shown by examples that they occur. There are a number of results stating that a type of Positivstellensatz is valid for $M_n(\\cA)$ provided that it holds for $\\cA$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-08-06T09:41:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B48",
      "15B33",
      "14P99"
    ],
    "keywords": [
      "positivstellensätze",
      "matrix algebra",
      "cyclic algebra",
      "formally real field",
      "unitary space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.1529S"
    }
  }
}