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Nonextreme de Branges–Rovnyak Spaces as Models for Contractions

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Abstract

The de Branges–Rovnyak spaces are known to provide an alternate functional model for contractions on a Hilbert space, equivalent to the Sz.-Nagy–Foias model. The scalar de Branges–Rovnyak spaces \({\mathcal{H}(b)}\) have essentially different properties, according to whether the defining function b is or not extreme in the unit ball of H ∞. For b extreme the model space is just \({\mathcal{H}(b)}\), while for b nonextreme an additional construction is required. In the present paper we identify the precise class of contractions which have as a model \({\mathcal{H}(b)}\) with b nonextreme.

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Authors and Affiliations

  1. Département de Mathématiques et de Statistique, Université Laval, Quebec, QC, G1K 7P4, Canada

    Javad Mashreghi

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania

    Dan Timotin

Authors
  1. Javad Mashreghi
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  2. Dan Timotin
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Correspondence to Dan Timotin.

Additional information

J. Mashreghi is supported by a grant from NSERC (Canada). D. Timotin is partially supported by a grant of the Romanian National Authority for Scientific Research, CNCS UEFISCDI, project number PN-II-ID-PCE-2011-3-0119.

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Mashreghi, J., Timotin, D. Nonextreme de Branges–Rovnyak Spaces as Models for Contractions. Integr. Equ. Oper. Theory 80, 137–152 (2014). https://doi.org/10.1007/s00020-014-2125-1

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  • DOI: https://doi.org/10.1007/s00020-014-2125-1

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