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Terry A. Loring

  1. Noncommutative Semialgebraic Sets in Nilpotent Variables.

    Чт, 01/13/2011 - 16:01 — SomNambul
    Authors: Terry A. Loring, Tatiana Shulman
    Subjects: Operator Algebras
    Abstract

    We solve the lifting problem in C^*-algebras for many sets of relations that
    include the relations x_j^{N_j} = 0 on each variable. The remaining relations
    must be of the form \| p(x_1,...,x_n) \| \leq C for C a positive constant and p
    a noncommutative *-polynomial that is in some sense homogeneous. For example,
    we prove liftability for the set of relations x^3=0, y^4=0, z^5=0,
    xx^*+yy^*+zz^* \leq 1. Thus we find more noncommutative semialgebraic sets that
    have the topology of noncommutative absolute retracts.

  2. Almost commuting self-adjoint matrices --- the real and self-dual cases.

    Пт, 12/17/2010 - 16:01 — SomNambul
    Authors: Terry A. Loring, Adam P. W. Sørensen
    Subjects: Operator Algebras
    Abstract

    We show that a pair of almost commuting self-adjoint, symmetric matrices are
    close to commuting self-adjoint, symmetric matrices (in a uniform way).
    Moreover we prove that the same holds with self-dual in place of symmetric.
    Since a symmetric self-adjoint matrix is real, the former gives a real version
    of Huaxin Lin's famous theorem on almost commuting matrices. There are
    applications to physics of Lin's original theorem and both new cases.

  3. Noncommutative Semialgebraic sets and Associated Lifting Problems.

    Пнд, 08/24/2009 - 13:10 — SomNambul
    Authors: Terry A. Loring, Tatiana Shulman
    Subjects: Operator Algebras
    Abstract

    We solve a class of lifting problems involving approximate polynomial
    relations (``softened polynomial relations''). Various associated C*-algebras
    are therefore projective. The technical lemma we need is a new manifestation of
    Akemann and Pedersen's discovery of the norm adjusting power of quasi-central
    approximate units.

  4. Weakly Projective C*-Algebras.

    Пнд, 08/24/2009 - 13:10 — SomNambul
    Authors: Terry A. Loring
    Subjects: Operator Algebras
    Abstract

    The noncommutative analog of an approximative absolute retract (AAR) is
    introduced, a weakly projective C*-algebra. This property sits between being
    residually finite dimensional and projectivity. There is a slightly weaker
    property that is the noncommutative analog of a pointed approximative absolute
    retract.

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