{
  "id": "math/9512207",
  "version": "v1",
  "published": "1995-12-14T00:00:00.000Z",
  "updated": "1995-12-14T00:00:00.000Z",
  "title": "Quadratic forms in unitary operators",
  "authors": [
    "Gilles Pisier"
  ],
  "journal": "Linear Algebra and its Applications. 267 (1997) 125-137.",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $u_1,\\ldots,u_n$ be unitary operators on a Hilbert space $H$. We study the norm $$\\left\\|\\sum^{i=n}_{i=1} u_i \\otimes \\bar u_i\\right\\|\\leqno (1)$$ of the operator $\\sum u_i \\otimes \\bar u_i$ acting on the Hilbertian tensor product $H\\otimes_2 \\overline H$. The main result of this note is Theorem 1. For any $n$-tuple $u_1,\\ldots, u_n$ of unitary operators in $B(H)$, we have $$2\\sqrt{n-1} \\le \\left\\|\\sum^n_1 u_i \\otimes \\bar u_i\\right\\|.\\leqno (6)$$ In other words, the right side of (6) is minimal exactly when $u_i = \\lambda(g_i)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1995-12-14T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unitary operators",
      "quadratic forms",
      "hilbertian tensor product",
      "right side",
      "hilbert space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1995math.....12207P"
    }
  }
}