{
  "id": "1410.6800",
  "version": "v1",
  "published": "2014-10-24T19:37:49.000Z",
  "updated": "2014-10-24T19:37:49.000Z",
  "title": "Convergence of functions of self-adjoint operators and applications",
  "authors": [
    "Lawrence G. Brown"
  ],
  "comment": "This paper is intended for a dual audience. Section 2, which contains the main result, is suitable for a general audience. Section 3 concerns technical operat or algebraic questions, though I have tried to present it with a minimum of tech nicality. As with all my papers, I welcome comments, especially for this paper, since I know almost nothing about Korovkin type theorems",
  "categories": [
    "math.FA"
  ],
  "abstract": "The main result (roughly) is that if (H_i) converges weakly to H and if also f(H_i) converges weakly to f(H), for a single strictly convex continuous function f, then (H_i) must converge strongly to H. One application is that if f(pr(H)) = pr(f(H)), where pr denotes compression to a closed subspace M, then M must be invariant for H. A consequence of this is the verification of a conjecture of Arveson, that Theorem 9.4 of [Arv] remains true in the infinite dimensional case. And there are two applications to operator algebras. If h and f(h) are both quasimultipliers, then h must be a multiplier. Also (still roughly stated) if h and f(h) are both in pA_sa p, for a closed projection p, then h must be strongly q-continuous on p.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-24T19:37:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B15",
      "47A60",
      "46L05"
    ],
    "keywords": [
      "self-adjoint operators",
      "application",
      "convergence",
      "single strictly convex continuous function",
      "pr denotes compression"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.6800B"
    }
  }
}