{
  "id": "2306.06248",
  "version": "v1",
  "published": "2023-06-09T20:43:26.000Z",
  "updated": "2023-06-09T20:43:26.000Z",
  "title": "A representation of sup-completion",
  "authors": [
    "Achintya Raya Polavarapu",
    "Vladimir G. Troitsky"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "It was showed by Donner in 1982 that every order complete vector lattice $X$ may be embedded into a cone $X^s$, called the sup-completion of $X$. We show that if one represents the universal completion of $X$ as $C^\\infty(K)$, then $X^s$ is the set of all continuous functions from $K$ to $[-\\infty,\\infty]$ that dominate some element of $X$. This provides a functional representation of $X^s$, as well as an easy alternative proof of its existence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-09T20:43:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46A40",
      "46E05"
    ],
    "keywords": [
      "sup-completion",
      "order complete vector lattice",
      "universal completion",
      "functional representation",
      "continuous functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}