{
  "id": "2310.12030",
  "version": "v1",
  "published": "2023-10-18T15:14:17.000Z",
  "updated": "2023-10-18T15:14:17.000Z",
  "title": "Banach spaces of sequences arising from infinite matrices",
  "authors": [
    "Arian Bërdëllima",
    "Naim L. Braha"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Given an infinite matrix $M=(m_{nk})$ we study a family of sequence spaces $\\ell_M^p$ associated with it. When equipped with a suitable norm $\\|\\cdot\\|_{M,p}$ we prove some basic properties of the Banach spaces of sequences $(\\ell_M^p,\\|\\cdot\\|_{M,p})$. In particular we show that such spaces are separable and strictly/uniformly convex for a considerably large class of infinite matrices $M$ for all $p>1$. A special attention is given to the identification of the dual space $(\\ell_M^p )^*$. Building on the earlier works of Bennett and J\\\"agers, we extend and apply some classical factorization results to the sequence spaces $\\ell_M^p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-18T15:14:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B45",
      "46B10",
      "46B20",
      "46B04",
      "46B03"
    ],
    "keywords": [
      "infinite matrix",
      "banach spaces",
      "sequences arising",
      "sequence spaces",
      "special attention"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}