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Maurice J. Dupré

  1. Differential algebras with Banach-algebra coefficients II: The operator cross-ratio tau-function and the Schwarzian derivative.

    Пнд, 04/11/2011 - 15:01 — SomNambul
    Authors: Emma Previato, Maurice J. Dupré, James F. Glazebrook
    Subjects: Operator Algebras
    Abstract

    Several features of an analytic (infinite-dimensional) Grassmannian of
    (commensurable) subspaces of a Hilbert space were developed in the context of
    integrable PDEs (KP hierarchy). We extended some of those features when
    polarized separable Hilbert spaces are generalized to a class of polarized
    Hilbert modules, in particular the Baker and tau-functions, which become
    operator-valued. Following from Part I we produce a pre-determinant structure
    for a class of tau-functions defined in the setting of the similarity class of
    projections of a certain Banach *-algebra.

  2. Differential algebras with Banach-algebra coefficients I: From C*-algebras to the K-theory of the spectral curve.

    Пнд, 04/11/2011 - 15:01 — SomNambul
    Authors: Emma Previato, Maurice J. Dupré, James F. Glazebrook
    Subjects: Operator Algebras
    Abstract

    We present an operator-coefficient version of Sato's infinite-dimensional
    Grassmann manifold, and tau-function. In this context, the Burchnall-Chaundy
    ring of commuting differential operators becomes a C*-algebra, to which we
    apply the Brown-Douglas-Fillmore theory, and topological invariants of the
    spectral ring become readily available. We construct KK classes of the spectral
    curve of the ring and, motivated by the fact that all isospectral
    Burchnall-Chaundy rings make up the Jacobian of the curve, we compare the
    (degree-1) K-homology of the curve with that of its Jacobian.

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