{
  "id": "1802.04081",
  "version": "v1",
  "published": "2018-02-12T14:48:49.000Z",
  "updated": "2018-02-12T14:48:49.000Z",
  "title": "Characterizations of Compact Operators on $\\ell_{p}$ Type Fractional Sets of Sequences",
  "authors": [
    "Faruk Özger"
  ],
  "comment": "13 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Among the sets of sequences studied, difference sets of sequences are probably the most common type of sets. This paper considers some $\\ell_{p}$ type fractional difference sequence spaces via Euler gamma function. Although we characterize compactness conditions on those spaces using the main tools of Hausdorff measure of noncompactness, we can only obtain sufficient conditions when the final space is $\\ell _{\\infty }$. However, we use some recent results to exactly characterize the classes of compact matrix operators when the final space is the set of bounded sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-12T14:48:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B45",
      "47B37"
    ],
    "keywords": [
      "type fractional sets",
      "compact operators",
      "type fractional difference sequence spaces",
      "characterizations",
      "final space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}