{
  "id": "2212.11659",
  "version": "v1",
  "published": "2022-12-22T13:05:09.000Z",
  "updated": "2022-12-22T13:05:09.000Z",
  "title": "A note on the essential numerical range of block diagonal operators",
  "authors": [
    "Luís Carvalho",
    "Cristina Diogo",
    "Sérgio Mendes",
    "Helena Soares"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this note we characterize the essential numerical range of a block diagonal o\\-pe\\-ra\\-tor $T=\\bigoplus_i T_i$ in terms of the numerical ranges $\\{W(T_i)\\}_i$ of its components. Specifically, the essential numerical range of $T$ is the convex hull of the limit superior of $\\{W(T_i)\\}_i$. This characterization can be simplified further. In fact, we prove the existence of a decomposition of $T$ for which the convex hull is not required.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-22T13:05:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A12"
    ],
    "keywords": [
      "essential numerical range",
      "block diagonal operators",
      "convex hull",
      "limit superior",
      "components"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}