{
  "id": "1608.03666",
  "version": "v1",
  "published": "2016-08-12T03:40:49.000Z",
  "updated": "2016-08-12T03:40:49.000Z",
  "title": "Power type $ξ$-asymptotically uniformly smooth norms",
  "authors": [
    "Ryan M Causey"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We extend a precise renorming result of Godefroy, Kalton, and Lancien regarding asymptotically uniformly smooth norms of separable Banach spaces with Szlenk index $\\omega$. For every ordinal $\\xi$, we characterize the operators, and therefore the Banach spaces, which admit a $\\xi$-asymptotically uniformly smooth norm with power type modulus and compute for those operators the best possible exponent in terms of the values of $Sz_\\xi(\\cdot, \\varepsilon)$. We also introduce the $\\xi$-Szlenk power type and investigate ideal and factorization properties of classes associated with the $\\xi$-Szlenk power type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-12T03:40:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "szlenk power type",
      "power type modulus",
      "regarding asymptotically uniformly smooth norms",
      "szlenk index",
      "separable banach spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}