{
  "id": "2401.03399",
  "version": "v1",
  "published": "2024-01-07T07:01:34.000Z",
  "updated": "2024-01-07T07:01:34.000Z",
  "title": "Some results on $E$-frames in Hilbert spaces",
  "authors": [
    "H. Hedayatirad",
    "T. L. Shateri"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The recently introduced concept of $E$-frames for a separable Hilbert space $\\mathcal{H}$, where E is an invertible infinite matrix mapping on the Hilbert space $\\bigoplus_{n=1}^{\\infty}\\mathcal{H}$, is a generalization of the notion of frames for $\\mathcal{H}$. In this paper, we have stated some results about this concept. Furthermore, we introduce the notion of controlled $E$-frames and we characterize all controlled $E$-duals associated with a given controlled $E$-frame.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-07T07:01:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C15",
      "54D55"
    ],
    "keywords": [
      "separable hilbert space",
      "invertible infinite matrix mapping",
      "generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}