{
  "id": "2006.11954",
  "version": "v1",
  "published": "2020-06-22T00:51:27.000Z",
  "updated": "2020-06-22T00:51:27.000Z",
  "title": "Invariant subspace problem for rank-one perturbations: the quantitative version",
  "authors": [
    "Adi Tcaciuc"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that for any bounded operator $T$ acting on infinite dimensional, complex Banach space, any for any $\\varepsilon>0$, there exists an operator $F$ of rank at most one such that $T+F$ has an invariant subspace of infinite dimension and codimension. A version of this result was proved in \\cite{T19} under additional spectral conditions for $T$ or $T^*$. This solves in full generality the quantitative version of the invariant subspace problem for rank-one perturbations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-22T00:51:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A15",
      "47A55"
    ],
    "keywords": [
      "invariant subspace problem",
      "rank-one perturbations",
      "quantitative version",
      "additional spectral conditions",
      "complex banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}