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Alejandro Varela

  1. Thompson-type formulae.

    Втр, 07/05/2011 - 15:01 — SomNambul
    Authors: Gabriel Larotonda, Jorge Antezana, Alejandro Varela
    Subjects: Functional Analysis
    Abstract

    Let X and Y be two nxn Hermitian matrices. In the article "Proof of a
    conjectured exponential formula" (Linear and Multilinear Algebra (19) 1986,
    187-197) R. C. Thompson proved that there exist two nxn unitary matrices U and
    V such that $$ e^{i X}e^{i Y}=e^{i (UXU^*+VBV^*)}. $$ In this note we consider
    extensions of this result to compact operators as well as to operators in an
    embeddable II$_1$ factor.

  2. Short paths for symmetric norms in the unitary group.

    Втр, 01/05/2010 - 16:01 — SomNambul
    Authors: Gabriel Larotonda, Jorge Antezana, Alejandro Varela
    Subjects: Metric Geometry
    Abstract

    For a given symmetrically normed ideal I on an infinite dimensional Hilbert
    space H, we study the rectifiable distance in the classical Banach-Lie unitary
    group $$ U_I={u is a unitary operator in H, u-1\in I}. $$ We prove that
    one-parameter subgroups of U_I are short paths, provided the spectrum of the
    exponent is bounded by $\pi$, and that any two elements of U_I can be joined
    with a short path, thus obtaining a Hopf-Rinow theorem in this infinite
    dimensional setting, for a wide and relevant class of (non necessarily smooth)
    metrics.

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