{
  "id": "1701.02916",
  "version": "v1",
  "published": "2017-01-11T10:29:06.000Z",
  "updated": "2017-01-11T10:29:06.000Z",
  "title": "On the extension of isometries between the unit spheres of a C*-algebra and B(H)",
  "authors": [
    "Francisco J. Fernández-Polo",
    "Antonio M. Peralta"
  ],
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "Given two complex Hilbert spaces $H$ and $K$, let $S(B(H))$ and $S(B(K))$ denote the unit spheres of the C$^*$-algebras $B(H)$ and $B(K)$ of all bounded linear operators on $H$ and $K$, respectively. We prove that every surjective isometry $f: S(B(K)) \\to S(B(H))$ admits an extension to a surjective complex linear or conjugate linear isometry $T: B(K)\\to B(H)$. This provides a positive answer to Tingley's problem in the setting of $B(H)$ spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-11T10:29:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B49",
      "46A22",
      "46B20",
      "46B04",
      "46A16",
      "46E40"
    ],
    "keywords": [
      "unit spheres",
      "complex hilbert spaces",
      "conjugate linear isometry",
      "surjective complex linear",
      "bounded linear operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}