{
  "id": "1704.04392",
  "version": "v1",
  "published": "2017-04-14T11:02:44.000Z",
  "updated": "2017-04-14T11:02:44.000Z",
  "title": "A note on triangular operators on Smooth Sequence Spaces",
  "authors": [
    "Elif Uyanık",
    "Murat H. Yurdakul"
  ],
  "comment": "5 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "For a scalar sequence {(\\theta_n)}_{n \\in \\mathbb{N}}, let C be the matrix defined by c_n^k = \\theta_{n-k+1} if n > k, c_n^k = 0 if n < k. The map between K\\\"{o}the spaces \\lambda(A) and \\lambda(B) is called a Cauchy Product map if it is determined by the triangular matrix C. In this note we introduced some necessary and sufficient conditions for a Cauchy Product map on a nuclear K\\\"{o}the space \\lambda(A) to nuclear G_1-space \\lambda(B) to be linear and continuous. Its transpose is also considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-14T11:02:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B37",
      "46A45"
    ],
    "keywords": [
      "smooth sequence spaces",
      "triangular operators",
      "cauchy product map",
      "scalar sequence",
      "triangular matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}