{
  "id": "math/9509213",
  "version": "v1",
  "published": "1995-09-10T00:00:00.000Z",
  "updated": "1995-09-10T00:00:00.000Z",
  "title": "A rearrangement invariant space isometric to $L_p$ coincides with $L_p$",
  "authors": [
    "Yuri A. Abramovich",
    "Mikhail Zaidenberg"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "The following theorem is the main result of this note. Theorem 1. Let $(E, \\|\\cdot\\|_E) $ be a rearrangement invariant Banach function space on the interval $[0, 1]$. If $E$ is isometric to $\\L_p [0, 1]$ for some $1\\le p<\\infty$, then $E$ coincides with $\\L_p [0, 1]$ and furthermore $\\|\\cdot\\|_E = \\lambda\\|\\cdot\\|_{\\L_p}$, where $\\lambda = \\|{\\bf 1}\\|_E$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1995-09-10T00:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E30"
    ],
    "keywords": [
      "rearrangement invariant space isometric",
      "rearrangement invariant banach function space",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1995math......9213A"
    }
  }
}