{
  "id": "2007.09145",
  "version": "v1",
  "published": "2020-07-17T07:45:58.000Z",
  "updated": "2020-07-17T07:45:58.000Z",
  "title": "A de Branges-Beurling theorem for the full Fock space",
  "authors": [
    "Robert T. W. Martin",
    "Eli Shamovich"
  ],
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "We extend the de Branges-Beurling theorem characterizing the shift-invariant spaces boundedly contained in the Hardy space of square-summable power series to the full Fock space over $\\mathbb{C} ^d$. Here, the full Fock space is identified as the \\emph{Non-commutative (NC) Hardy Space} of square-summable Taylor series in several non-commuting variables. We then proceed to study lattice operations on NC kernels and operator-valued multipliers between vector-valued Fock spaces. In particular, we demonstrate that the operator-valued Fock space multipliers with common coefficient range space form a bounded general lattice modulo a natural equivalence relation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-17T07:45:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "full fock space",
      "branges-beurling theorem",
      "common coefficient range space form",
      "hardy space",
      "study lattice operations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}