{
  "id": "2409.14068",
  "version": "v1",
  "published": "2024-09-21T08:47:09.000Z",
  "updated": "2024-09-21T08:47:09.000Z",
  "title": "Operators on anti-dual pairs: Lebesgue decomposition via Arlinskii's iteration",
  "authors": [
    "Ábel Göde",
    "Zsigmond Tarcsay"
  ],
  "comment": "13 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "The aim of this paper is to prove a general Lebesgue decomposition theorem for positive operators on so-called anti-dual pairs, following the iterative approach introduced by Arlinskii. This procedure and the resulting theorem encompass several special cases, including positive operators on Hilbert spaces, non-negative forms on vector spaces, and representable functionals over *-algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-21T08:47:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B65",
      "47A07"
    ],
    "keywords": [
      "anti-dual pairs",
      "arlinskiis iteration",
      "general lebesgue decomposition theorem",
      "positive operators",
      "resulting theorem encompass"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}