{
  "id": "1905.09592",
  "version": "v1",
  "published": "2019-05-23T11:33:28.000Z",
  "updated": "2019-05-23T11:33:28.000Z",
  "title": "Escaping a neighborhood along a prescribed sequence in Lie groups and Banach algebras",
  "authors": [
    "Catalin Badea",
    "Vincent Devinck",
    "Sophie Grivaux"
  ],
  "comment": "20 pages",
  "categories": [
    "math.FA",
    "math.GR",
    "math.MG"
  ],
  "abstract": "It is shown that Jamison sequences, introduced in [C. Badea and S. Grivaux, Unimodular eigenvalues, uniformly distributed sequences and linear dynamics, Adv. Math. 211 (2007), no. 2, 766--793], arise naturally in the study of topological groups with no small subgroups, of Banach algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of its powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or Banach algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given and other related results are proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-23T11:33:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A10",
      "47A12",
      "47A60",
      "22E15"
    ],
    "keywords": [
      "lie groups",
      "prescribed sequence",
      "jamison sequences",
      "banach algebras escape",
      "banach algebra elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}