{
  "id": "2412.14808",
  "version": "v1",
  "published": "2024-12-19T12:57:10.000Z",
  "updated": "2024-12-19T12:57:10.000Z",
  "title": "Extension of Norm One Projections",
  "authors": [
    "Xiangdi Fu",
    "Dilong Li"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Through the establishment of several extension theorems, we provide explicit expressions for norm one projections and 1-complemented subspaces in the Hardy space $H^p(\\mathbb{T})$ for $1\\leq p<\\infty$, $p\\neq 2$. Our characterization leads to two significant corollaries: first, all 1-complemented subspaces of $H^p(\\mathbb{T})$ with dimension greater than one are isometric to $H^p(\\mathbb{T})$; second, all norm one projections on $H^p(\\mathbb{T})$ are restrictions of norm one projections on $L^p(\\mathbb{T})$ that leave $H^p(\\mathbb{T})$ invariant. The second corollary answers an open problem posed by P. Wojtaszczyk in 2003. Moreover, this is the first time that norm one projections and 1-complemented subspaces in an analytic function space have been completely understood.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-19T12:57:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "projections",
      "analytic function space",
      "second corollary answers",
      "explicit expressions",
      "first time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}