{
  "id": "2005.01150",
  "version": "v1",
  "published": "2020-05-03T17:26:47.000Z",
  "updated": "2020-05-03T17:26:47.000Z",
  "title": "Invariant subspaces for positive operators on Banach spaces with unconditional basis",
  "authors": [
    "Eva A. Gallardo-Gutiérrez",
    "Javier González-Doña",
    "Pedro Tradacete"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that every lattice homomorphism acting on a Banach space $\\mathcal{X}$ with the lattice structure given by an unconditional basis has a non-trivial closed invariant subspace. In fact, it has a non-trivial closed invariant ideal, which is no longer true for every positive operator on such a space. Motivated by these later examples, we characterize tridiagonal positive operators without non-trivial closed invariant ideals on $\\mathcal{X}$ extending to this context a result of Grivaux on the existence of non-trivial closed invariant subspaces for tridiagonal operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-03T17:26:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46A40",
      "46B40",
      "47B60"
    ],
    "keywords": [
      "unconditional basis",
      "banach space",
      "non-trivial closed invariant subspace",
      "non-trivial closed invariant ideal",
      "longer true"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}