{
  "id": "1512.07483",
  "version": "v1",
  "published": "2015-12-23T14:16:06.000Z",
  "updated": "2015-12-23T14:16:06.000Z",
  "title": "Growth rates and the peripheral spectrum of positive operators",
  "authors": [
    "Jochen Glück"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $T$ be a positive operator on a complex Banach lattice. It is a long open problem whether the peripheral spectrum $\\sigma_{\\operatorname{per}}(T)$ of $T$ is always cyclic. We consider several growth conditions on $T$, involving its resolvent or its eigenvectors, and show that these conditions provide new sufficient criteria for cyclicity the peripheral spectrum of $T$. Moreover we give an alternative proof of the recent result that every (WS)-bounded operator has cyclic peripheral spectrum. We also consider irreducible operators $T$. If such an operator is Abel bounded, then it is known that every peripheral eigenvalue of $T$ is algebraically simple. We show that the same is true if $T$ only fulfils the weaker condition of being (WS)-bounded.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-23T14:16:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B65",
      "47A10",
      "46B42"
    ],
    "keywords": [
      "positive operator",
      "growth rates",
      "cyclic peripheral spectrum",
      "complex banach lattice",
      "long open problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}