{
  "id": "math/9508207",
  "version": "v1",
  "published": "1995-08-01T00:00:00.000Z",
  "updated": "1995-08-01T00:00:00.000Z",
  "title": "Vector-valued Walsh-Paley martingales and geometry of Banach spaces",
  "authors": [
    "Joerg Wenzel"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The concept of Rademacher type $p$ ($1\\leq p\\leq2$) plays an important role in the local theory of Banach spaces. In \\cite{mas88} Mascioni considers a weakening of this concept and shows that for a Banach space $X$ weak Rademacher type $p$ implies Rademacher type $r$ for all $r<p$. As with Rademacher type $p$ and weak Rademacher type $p$, we introduce the concept of Haar type $p$ and weak Haar type $p$ by replacing the Rademacher functions by the Haar functions in the respective definitions. We show that weak Haar type $p$ implies Haar type $r$ for all $r<p$. This solves a problem left open by Pisier \\cite{pis75}. The method is to compare Haar type ideal norms related to different index sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1995-08-01T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "banach space",
      "vector-valued walsh-paley martingales",
      "weak rademacher type",
      "weak haar type",
      "type ideal norms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1995math......8207W"
    }
  }
}