{
  "id": "math/9404209",
  "version": "v1",
  "published": "1994-04-14T16:07:37.000Z",
  "updated": "1994-04-14T16:07:37.000Z",
  "title": "Factorization and Reflexivity on Fock spaces",
  "authors": [
    "Alvaro Arias",
    "Gelu Popescu"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The framework of the paper is that of the full Fock space ${\\Cal F}^2({\\Cal H}_n)$ and the Banach algebra $F^\\infty$ which can be viewed as non-commutative analogues of the Hardy spaces $H^2$ and $H^\\infty$ respectively. An inner-outer factorization for any element in ${\\Cal F}^2({\\Cal H}_n)$ as well as characterization of invertible elements in $F^\\infty$ are obtained. We also give a complete characterization of invariant subspaces for the left creation operators $S_1,\\cdots, S_n$ of ${\\Cal F}^2({\\Cal H}_n)$. This enables us to show that every weakly (strongly) closed unital subalgebra of $\\{\\varphi(S_1,\\cdots,S_n):\\varphi\\in F^\\infty\\}$ is reflexive, extending in this way the classical result of Sarason [S]. Some properties of inner and outer functions and many examples are also considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1994-04-14T16:07:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reflexivity",
      "full fock space",
      "left creation operators",
      "hardy spaces",
      "inner-outer factorization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1994math......4209A"
    }
  }
}