{
  "id": "2203.01301",
  "version": "v1",
  "published": "2022-03-02T18:34:41.000Z",
  "updated": "2022-03-02T18:34:41.000Z",
  "title": "Frames of iterations and vector-valued model spaces",
  "authors": [
    "Carlos Cabrelli",
    "Ursula Molter",
    "Daniel Suárez"
  ],
  "comment": "21 pages",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "Let T be a bounded operator on a Hilbert space H, and F = {f_j: j in J} an at most countable set of vectors in H. In this note, we characterize the pairs {T, F} such that {T^n f: f in F, n in I} form a frame of H, for the cases of I = N_0 and I = Z. The characterization for unilateral iterations gives a similarity with the compression of the shift acting on model spaces of the Hardy space of analytic functions defined on the unit disk with values in $l^2(J). This generalizes recent work for iterations of a single function. In the case of bilateral iterations, the characterization is by the bilateral shift acting on doubly invariant subspaces of L^2(T,l^2(J)). Furthermore, we characterize the frames of iterations for vector-valued model operators when J is finite in terms of Toeplitz and multiplication operators in the unilateral and bilateral case, respectively. Finally, we study the problem of finding the minimal number of orbits that produce a frame in this context.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-02T18:34:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vector-valued model spaces",
      "unilateral iterations",
      "shift acting",
      "hardy space",
      "analytic functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}