{
  "id": "math/9812062",
  "version": "v1",
  "published": "1998-12-09T21:29:23.000Z",
  "updated": "1998-12-09T21:29:23.000Z",
  "title": "Injective isometries in Orlicz spaces",
  "authors": [
    "Beata Randrianantoanina"
  ],
  "comment": "20 pages, 2 figures, to appear in the Proceedings of the Third Conference on Function Spaces held in Edwardsville in May 1998, Contemporary Math",
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that injective isometries in Orlicz space $L_M$ have to preserve disjointness, provided that Orlicz function $M$ satisfies $\\Delta_2$-condition, has a continuous second derivative $M''$, satisfies another ``smoothness type'' condition and either $\\lim_{t\\to0} M''(t) = \\infty$ or $M''(0) = 0$ and $M''(t)>0$ for all $t>0$. The fact that surjective isometries of any rearrangement-invariant function space have to preserve disjointness has been determined before. However dropping the assumption of surjectivity invalidates the general method. In this paper we use a differential technique.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-12-09T21:29:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "orlicz space",
      "injective isometries",
      "preserve disjointness",
      "rearrangement-invariant function space",
      "orlicz function"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....12062R"
    }
  }
}