{
  "id": "2311.16757",
  "version": "v1",
  "published": "2023-11-28T13:01:10.000Z",
  "updated": "2023-11-28T13:01:10.000Z",
  "title": "Discrete Translates of an Operator in the Schatten $p$-Classes",
  "authors": [
    "Bhawna Dharra",
    "S. Sivananthan",
    "D. Venku Naidu"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this manuscript, we investigate the properties of systems formed by translations of an operator in the Schatten $p$-classes $\\mathcal{T}^p$. We establish the existence of Schauder frames of integer translates in $\\mathcal{T}^p$ for $p>2$. Later, we provide an instance of a uniformly discrete $\\Lambda \\subset \\mathbb{R}^{2d}$ such that there exists an operator whose $\\Lambda$-translates are complete in $\\mathcal{T}^p$ for all $p>1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-28T13:01:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B90",
      "42C15",
      "47B10"
    ],
    "keywords": [
      "discrete translates",
      "schauder frames",
      "integer translates",
      "manuscript"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}