{
  "id": "1807.01003",
  "version": "v1",
  "published": "2018-07-03T07:44:09.000Z",
  "updated": "2018-07-03T07:44:09.000Z",
  "title": "A short note on band projections in partially ordered vector spaces",
  "authors": [
    "Jochen Glück"
  ],
  "comment": "6 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Consider an Archimedean partially ordered vector space $X$ with generating cone (or, more generally, a pre-Riesz space $X$). Let $P$ be a linear projection on $X$ such that both $P$ and its complementary projection $I - P$ are positive; we prove that the range of $P$ is a band. This shows that the well-known concept of band projections on vector lattices can, to a certain extent, be transferred to the framework of ordered vector spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-03T07:44:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B60",
      "47B65"
    ],
    "keywords": [
      "band projections",
      "short note",
      "archimedean partially ordered vector space",
      "pre-riesz space",
      "linear projection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}