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Marc A. Rieffel

  1. Distances between matrix algebras that converge to coadjoint orbits.

    Втр, 10/13/2009 - 18:46 — SomNambul
    Authors: Marc A. Rieffel
    Subjects: Operator Algebras
    Abstract

    For any sequence of matrix algebras that converge to a coadjoint orbit we
    give explicit formulas that show that the distances between the matrix algebras
    (viewed as quantum metric spaces) converges to 0. In the process we develop a
    general point of view that is likely to be useful in other related settings.

  2. Distances between matrix algebras that converge to coadjoint orbits.

    Втр, 10/13/2009 - 18:46 — SomNambul
    Authors: Marc A. Rieffel
    Subjects: Operator Algebras
    Abstract

    For any sequence of matrix algebras that converge to a coadjoint orbit we
    give explicit formulas that show that the distances between the matrix algebras
    (viewed as quantum metric spaces) converges to 0. In the process we develop a
    general point of view that is likely to be useful in other related settings.

  3. Leibniz seminorms for "Matrix algebras converge to the sphere''.

    Пт, 08/28/2009 - 23:56 — SomNambul
    Authors: Marc A. Rieffel
    Subjects: Operator Algebras
    Abstract

    In an earlier paper of mine relating vector bundles and Gromov-Hausdorff
    distance for ordinary compact metric spaces, it was crucial that the Lipschitz
    seminorms from the metrics satisfy a strong Leibniz property. In the present
    paper, for the now non-commutative situation of matrix algebras converging to
    the sphere (or to other spaces) for quantum Gromov-Hausdorff distance, we show
    how to construct suitable seminorms that also satisfy the strong Leibniz
    property.

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