{
  "id": "2003.11567",
  "version": "v1",
  "published": "2020-03-25T18:06:28.000Z",
  "updated": "2020-03-25T18:06:28.000Z",
  "title": "On Banach algebras of band-dominated operators and their order structure",
  "authors": [
    "Bruno de Mendonça Braga"
  ],
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "The goal of this paper is to study band-dominated operators on Banach spaces with Schauder basis with respect to uniformly locally finite metric spaces as well as the Banach algebras generated by them: the so called uniform Roe algebras. We investigate several kinds of isomorphisms between those Banach spaces (e.g., isomorphisms preserving norm, order, algebraic structure, etc) and prove several rigidity results on when a certain kind of isomorphism between the uniform Roe algebras implies that the base metric spaces are (bijectively) coarsely equivalent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-25T18:06:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "banach algebras",
      "band-dominated operators",
      "order structure",
      "banach spaces",
      "uniform roe algebras implies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}