{
  "id": "math/0110315",
  "version": "v1",
  "published": "2001-10-30T16:50:21.000Z",
  "updated": "2001-10-30T16:50:21.000Z",
  "title": "Manifolds of algebraic elements in the algebra L(H) of bounded linear operators",
  "authors": [
    "Jose M. Isidro"
  ],
  "comment": "12 pages, Latex 2e, to appear",
  "categories": [
    "math.FA",
    "math.DG"
  ],
  "abstract": "Given a complex Hilbert space H, we study the differential geometry of the manifold A of normal algebraic elements in Z=L(H), the algebra of bounded linear operators on H. We represent A as a disjoint union of subsets M of Z and, using the algebraic structure of Z, a torsionfree affine connection $\\nabla$ (that is invariant under the group G= Aut (Z) of automorphisms of Z) is defined on each of these connected components and the geodesics are computed. In case M consists of elements that have a fixed finite rank r, (0<r<\\infty), G-invariant Riemann and K\\\"ahler structures are defined on M which in this way becomes a totally geodesic symmetric holomorphic manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-10-30T16:50:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "48G20",
      "72H51"
    ],
    "keywords": [
      "bounded linear operators",
      "totally geodesic symmetric holomorphic manifold",
      "torsionfree affine connection",
      "normal algebraic elements",
      "complex hilbert space"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....10315I"
    }
  }
}