{
  "id": "1503.07334",
  "version": "v1",
  "published": "2015-03-25T11:17:19.000Z",
  "updated": "2015-03-25T11:17:19.000Z",
  "title": "Dilations of matricies",
  "authors": [
    "David Cohen"
  ],
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "We explore aspects of dilation theory in the finite dimensional case and show that for a commuting $n$-tuple of operators $T=(T_1,...,T_n) $ acting on some finite dimensional Hilbert space $H$ and a compact set $X\\subset \\mathbb{C}^n$ the following are equivalent: 1. $T$ has a normal $ X$-dilation. 2. For any $m\\in \\mathbb{N}$ there exists some finite dimensional Hilbert space $K$ containing $H$ and a tuple of commuting normal operators $N=(N_1,...,N_n)$ acting on $K$ such that $$ q(T)=P_Hq(N)|_H$$ for all polynomials $q$ of degree at most $m$ and such that the joint spectrum of $N$ is contained in $X$ (where $P_H$ is the projection from $K$ to $H$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-25T11:17:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite dimensional hilbert space",
      "finite dimensional case",
      "dilation theory",
      "joint spectrum",
      "commuting normal operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}