OPERATOR THEORY SEMINAR

    SPRING 2007




    Bill Ross, November 14, 2006




    The gang in Tom Kriete's office, November 14, 2006. Left to right: Katie Quertermous, Katherine Heller, Rebecca Schmitz, Bill Duren, Matthew Pons, and Tom Kriete

    RECENT PAST SCHEDULES:

    Spring 2006 , Fall 2006
    Spring 2005 , Fall 2005
    Spring 2004 , Fall 2004
    Spring 2003 , Fall 2003
    Fall 2002

    The seminar meets Tuesdays 3:30-4:30 PM in KER 326. Special lectures outside this hour may be announced from time to time.

    Feb. 19-23

    Tuesday, Feb. 20
    James Rovnyak
    Schwarz-Pick inequalities for the Schur-Agler class on the polydisk and unit ball

    Feb. 26 - Mar. 2

    Tuesday, Feb. 27
    James Rovnyak
    Schwarz-Pick inequalities for the Schur-Agler class on the polydisk and unit ball, continued

    Mar. 5-9

    Tuesday, Mar. 6
    NO MEETING: SPRING BREAK
    Title

    Mar. 12-16

    SPECIAL LECTURES

    Monday, March 12, 2 PM
    Anna-Maria Persson, University of Lund
    On the spectrum of the Cesaro operator on spaces of analytic functions

    Monday, March 12, 3:30 PM
    Marcus Carlsson, University of Lund
    On the index of invariant subspaces in spaces of vector-valued analytic functions

    Mar. 19-23

    Tuesday, Mar. 20
    James Rovnyak
    Schwarz-Pick inequalities for the Schur-Agler class on the polydisk and unit ball, continued

    Mar. 26-30

    SPECIAL LECTURE

    Friday, March 30, 3:30 PM, KER 205
    Joe Ball, Virginia Tech
    Models for commuting pairs of Hilbert space contraction operators

    The Sz.-Nagy dilation theorem asserts that any contraction operator T on a Hilbert space H can be dilated to a unitary operator U on a larger Hilbert space K. Later versions of this dilation theorem give a detailed picture of the geometry of how the original space H sits inside the dilation space K. This geometry in turn leads simultaneously to the Sz.-Nagy-Foias model for the contraction operator T and to a discrete-time Lax-Phillips scattering system with unitary evolution given by U. Moreover, the dilation space K can be identified with the space of finite-energy trajectories of an embedded discrete-time, conservative, input/state/output linear system. The system matrix for the input/state/output linear system, with appropriate minimality assumptions, is just a Halmos dilation (Julia operator) for the contraction operator T. Each of these three paradigms has a functional model determined by the same Schur-class function on the unit disk (the Sz.-Nagy-Foias characteristic function for T, the scattering matrix for the Lax-Phillips scattering system, and the transfer function for the input/state/output linear system). In this talk I will discuss recent progress on finding an analogue of all these ideas for the case where the single contraction operator T is replaced by a commuting pair of contractions (T1,T2). The Ando dilation theorem giving a commuting unitary-pair dilation (U1,U2) for a commuting contractive pair (T1,T2) is just the first step. This reports on joint work with Victor Vinnikov of Ben Gurion University.

    Apr. 2-6

    Tuesday, Apr. 3
    James Rovnyak
    Operator identities in the study of canonical differential systems
    Beamer lecture

    Apr. 9-13

    Tuesday, Apr. 10
    Katherine Heller
    Adjoints of composition operators on Hilbert spaces of analytic functions

    Apr. 16-20

    Tuesday, Apr. 17
    No lecture


    Apr. 23-27

    Tuesday, Apr. 3
    No lecture


    Apr. 30 - May 4

    Tuesday, May 1
    Vladimir Bolotnikov, The College of William and Mary
    Carathéodory-Julia type theorems for operator-valued Schur functions
    Abstract