Friday, January 19, 2018 — 2:30 PM EST

Robert Martin, University of Cape Town

"A multi-variable de Branges-Rovnyak model for row contractions"

In the operator-model theory of de Branges and Rovnyak, any completely non-coisometric (CNC) contraction on Hilbert space is represented as the adjoint of the restriction of the backward shift to a de Branges-Rovnyak subspace of the classical (vector-valued) Hardy space of analytic functions in the open unit disk. We provide a natural extension of this model to the setting of CNC (row) contractions from several copies of a Hilbert space into itself. A canonical extension of Hardy space to several complex dimensions is the Drury-Arveson space, and the appropriate analogue of the adjoint of the restriction of the backward shift to a de Branges-Rovnyak space is a Gleason solution, a row contraction which acts as a several-variable difference quotient. Our several-variable model completely characterizes the class of all CNC row contractions which can be represented as (extremal contractive) Gleason solutions for a multi-variable de Branges-Rovnyak subspace of (vector-valued) Drury-Arveson space.

References

  1. R.T.W. Martin and A. Ramanantoanina. A Gleason solution model for row contractions. To appear in Oper. Theory Adv. Appl., volume dedicated to J.A. Ball, 2018.
  2. A. Ramanantoanina. Gleason solutions and canonical models for row contractions. Master's thesis, University of Cape Town, 2017.

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