{
  "id": "math/0211359",
  "version": "v1",
  "published": "2002-11-22T16:08:04.000Z",
  "updated": "2002-11-22T16:08:04.000Z",
  "title": "Total Dilations",
  "authors": [
    "Jean-Christophe Bourin"
  ],
  "comment": "12 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "(1) Let $A$ be an operator on a space ${\\cal H}$ of even finite dimension. Then for some decomposition ${\\cal H}={\\cal F}\\oplus{\\cal F}^{\\perp}$, the compressions of $A$ onto ${\\cal F}$ and ${\\cal F}^{\\perp}$ are unitarily equivalent. (2) Let $\\{A_j\\}_{j=0}^n$ be a family of strictly positive operators on a space ${\\cal H}$. Then, for some integer $k$, we can dilate each $A_j$ into a positive operator $B_j$ on $\\oplus^k{\\cal H}$ in such a way that: (i) The operator diagonal of $B_j$ consists of a repetition of $A_j$. (ii) There exist a positive operator $B$ on $\\oplus^k{\\cal H}$ and an increasing function $f_j : (0,\\infty)\\longrightarrow(0,\\infty)$ such that $B_j=f_j(B)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-11-22T16:08:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A20"
    ],
    "keywords": [
      "total dilations",
      "finite dimension",
      "operator diagonal",
      "decomposition",
      "compressions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....11359B"
    }
  }
}