{
  "id": "math/0304253",
  "version": "v1",
  "published": "2003-04-18T13:00:22.000Z",
  "updated": "2003-04-18T13:00:22.000Z",
  "title": "A generalization of Levinger's theorem to positive kernel operators",
  "authors": [
    "Roman Drnovšek"
  ],
  "comment": "11 pages. To appear in Glasgow Math. J",
  "journal": "Glasgow Math. J. 45 (2003), no. 3, 545-555",
  "doi": "10.1017/S0017089503001459",
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove some inequalities for the spectral radius of positive operators on Banach function spaces. In particular, we show the following extension of Levinger's theorem. Let $K$ be a positive compact kernel operator on $L^2(X,\\mu)$ with the spectral radius $r(K)$. Then the function $\\phi$ defined by $\\phi(t) = r(t K + (1-t) K^*)$ is non-decreasing on $[0, {1/2}]$. We also prove that $\\| A + B^* \\| \\ge 2 \\cdot \\sqrt{r(A B)}$ for any positive operators $A$ and $B$ on $L^2(X,\\mu)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-04-18T13:00:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive kernel operators",
      "levingers theorem",
      "generalization",
      "spectral radius",
      "banach function spaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......4253D"
    }
  }
}