{
  "id": "2212.08940",
  "version": "v1",
  "published": "2022-12-17T20:09:13.000Z",
  "updated": "2022-12-17T20:09:13.000Z",
  "title": "On The Frames In Hilbert $C^{\\ast}$-modules",
  "authors": [
    "M'hamed Ghiati",
    "Mohammed Mouniane",
    "Mohamed Rossafi"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1806.03993",
  "categories": [
    "math.FA"
  ],
  "abstract": "Frame theory has been rapidly generalized and various generalizations have been developed. In this paper, we present a brief survey of the frames in Hilbert $C^{\\ast}$-modules, including frames, $\\ast$-frames, g-frames, $\\ast$-g-frames, $\\ast$-$K$-g-frame, operator frame and $\\ast$-$K$-operator in Hilbert $C^{\\ast}$-modules. Various proofs are given for some results. Also, we prove some new results. Moreover, non-trivial examples are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-17T20:09:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C15",
      "47A05"
    ],
    "keywords": [
      "frame theory",
      "brief survey",
      "operator frame",
      "non-trivial examples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}