{
  "id": "2303.17994",
  "version": "v1",
  "published": "2023-03-31T12:11:21.000Z",
  "updated": "2023-03-31T12:11:21.000Z",
  "title": "Helson-Lowdenslager and de Branges type theorems in the setting of continuous rotationally symmetric norms",
  "authors": [
    "Apoorva Singh",
    "Niteesh Sahni"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "A Helson-Lowdenslager type result has been proved by Chen in the context of Lebesgue spaces of the unit circle equipped with a continuous rotationally symmetric norm by studying the simply invariant subspaces of the operator of multiplication by the coordinate function $z$. In this paper, we generalize Chen's result by obtaining a description of simply invariant subspaces for multiplication by $z^n$. A de Branges type result is also proved for Hardy spaces equipped with continuous rotationally symmetric norms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-31T12:11:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A15",
      "30H10",
      "47B38"
    ],
    "keywords": [
      "continuous rotationally symmetric norm",
      "branges type theorems",
      "simply invariant subspaces",
      "branges type result",
      "helson-lowdenslager type result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}