{
  "id": "1211.2089",
  "version": "v2",
  "published": "2012-11-09T10:05:04.000Z",
  "updated": "2017-10-25T16:38:38.000Z",
  "title": "Almost-additive ergodic theorems for amenable groups",
  "authors": [
    "Felix Pogorzelski"
  ],
  "comment": "Corrected version: Proposition 7.10 of the previous version removed, the assumption of approximability added in the pointwise ergodic theorem for bounded, additive processes (Theorem 7.12 in the new, Theorem 7.11 in the old version). Minor corrections and reference updates added as well",
  "journal": "Journal of Functional Analysis, 265 (8), 2013 Corrigendum and Addendum: Journal of Functional Analysis, 271 (11), 2016",
  "categories": [
    "math.DS",
    "math.FA",
    "math.SP"
  ],
  "abstract": "In this paper we prove a general convergence theorem for almost-additive set functions on unimodular, amenable groups. These mappings take their values in some Banach space. By extending the theory of epsilon-quasi tiling techniques, we set the ground for far-reaching applications in the theory of group dynamics. In particular, we verify the almost-everywhere convergence of abstract approximable bounded, additive processes, as well as a Banach space approximation result for the spectral distribution function (integrated density of states) for random operators on discrete structures in a metric space. Further, we include a Banach space valued version of the Lindenstrauss ergodic theorem for amenable groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-09T10:05:04.000Z",
      "abstract": "In this paper we prove a general convergence theorem for almost-additive set functions on unimodular, amenable groups. These mappings take their values in some Banach space. By extending the theory of epsilon-quasi tiling techniques, we set the ground for far-reaching applications in the theory of group dynamics. In particular, we verify the almost-everywhere convergence of abstract bounded, additive processes, as well as a Banach space approximation result for the spectral distribution function (integrated density of states) for random operators on discrete structures in a metric space. Further, we include a Banach space valued version of the Lindenstrauss ergodic theorem for amenable groups.",
      "comment": "47 pages",
      "journal": "Journal of Functional Analysis, 265 (8), 2013",
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2017-10-25T16:38:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "amenable groups",
      "almost-additive ergodic theorems",
      "banach space approximation result",
      "lindenstrauss ergodic theorem",
      "banach space valued version"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.2089P"
    }
  }
}