{
  "id": "math/0003152",
  "version": "v1",
  "published": "2000-03-24T18:00:36.000Z",
  "updated": "2000-03-24T18:00:36.000Z",
  "title": "Perturbation of $l^1$-copies and measure convergence in preduals of von Neumann algebras",
  "authors": [
    "Hermann Pfitzner"
  ],
  "comment": "submitted to J. of Op. Th",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let L_1 be the predual of a von Neumann algebra with a finite faithful normal trace. We show that a bounded sequence in L_1 converges to 0 in measure if and only if each of its subsequences admits another subsequence which converges to 0 in norm or spans $l^1$ \"almost isometrically\". Furthermore we give a quantitative version of an essentially known result concerning the perturbation of a sequence spanning $l^1$ isomorphically in the dual of a C$^*$-algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-03-24T18:00:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B20",
      "46L05"
    ],
    "keywords": [
      "von neumann algebra",
      "measure convergence",
      "perturbation",
      "finite faithful normal trace",
      "subsequences admits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......3152P"
    }
  }
}