{
  "id": "2204.13964",
  "version": "v1",
  "published": "2022-04-29T09:25:42.000Z",
  "updated": "2022-04-29T09:25:42.000Z",
  "title": "Analyticity of positive semigroups is inherited under domination",
  "authors": [
    "Jochen Glück"
  ],
  "comment": "4 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "For positive $C_0$-semigroups $S$ and $T$ on a Banach lattice such that $S(t) \\le T(t)$ for all times $t$, we prove that analyticity of $T$ implies analyticity of $S$. This answers an open problem posed by Arendt in 2004. Our proof is based on a spectral theoretic argument: we apply Perron-Frobenius theory to multiplication operators that are induced by $S$ and $T$ on a vector-valued function space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-29T09:25:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D06",
      "47B65",
      "47A10"
    ],
    "keywords": [
      "positive semigroups",
      "domination",
      "spectral theoretic argument",
      "banach lattice",
      "vector-valued function space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}