{
  "id": "2409.04866",
  "version": "v1",
  "published": "2024-09-07T16:35:58.000Z",
  "updated": "2024-09-07T16:35:58.000Z",
  "title": "Isomorphisms between vector-valued $H_p$-spaces for $0<p\\le 1$ and uniqueness of unconditional structure",
  "authors": [
    "Fernando Albiac",
    "Jose L. Ansorena"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The aim of this paper is twofold. On the one hand, we manage to identify Banach-valued Hardy spaces of analytic functions over the disc $\\mathbb{D}$ with other classes of Hardy spaces, thus complementing the existing literature on the subject. On the other hand, we develop new techniques that allow us to prove that certain Hilbert-valued atomic lattices have a unique unconditional basis, up to normalization, equivalence and permutation. Combining both lines of action we show that that $H_p(\\mathbb{D},\\ell_2)$ for $0<p<1$ has a unique atomic lattice structure. The proof of this result relies on the validity of some new lattice estimates for non-locally convex spaces which hold an independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-07T16:35:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B15",
      "46B20",
      "46B42",
      "46B45",
      "46A16",
      "46A35",
      "46A40",
      "46A45"
    ],
    "keywords": [
      "unconditional structure",
      "isomorphisms",
      "uniqueness",
      "unique atomic lattice structure",
      "unique unconditional basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}