{
  "id": "0903.5412",
  "version": "v1",
  "published": "2009-03-31T12:28:09.000Z",
  "updated": "2009-03-31T12:28:09.000Z",
  "title": "Invariant subspaces for operator semigroups with commutators of rank at most one",
  "authors": [
    "Roman Drnovšek"
  ],
  "comment": "10 pages; to appear in Journal of Functional Analysis",
  "journal": "J. Funct. Anal. 256 (2009), no. 12, 4187-4196",
  "doi": "10.1016/j.jfa.2009.03.010",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let X be a complex Banach space of dimension at least 2, and let S be a multiplicative semigroup of operators on X such that the rank of AB - BA is at most 1 for all pairs {A,B} in S. We prove that S has a non-trivial invariant subspace provided it is not commutative. As a consequence we show that S is triangularizable if it consists of polynomially compact operators. This generalizes results from [H. Radjavi, P. Rosenthal, From local to global triangularization, J. Funct. Anal. 147 (1997), 443-456] and [G. Cigler, R. Drnov\\v{s}ek, D. Kokol-Bukov\\v{s}ek, T. Laffey, M. Omladi\\v{c}, H. Radjavi, P. Rosenthal, Invariant subspaces for semigroups of algebraic operators, J. Funct. Anal. 160 (1998), 452-465].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-31T12:28:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A15",
      "47D03"
    ],
    "keywords": [
      "operator semigroups",
      "commutators",
      "complex banach space",
      "non-trivial invariant subspace",
      "global triangularization"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.5412D"
    }
  }
}