64 research outputs found

    Nonextreme de Branges-Rovnyak spaces as models for contractions

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    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 H(b)\mathcal{H}(b) have essentially different properties, according to whether the defining function bb is or not extreme in the unit ball of H∞H^\infty. For bb extreme the model space is just H(b)\mathcal{H}(b), while for bb nonextreme an additional construction is required. In the present paper we identify the precise class of contractions which have as a model H(b)\mathcal{H}(b) with bb nonextreme.Comment: 15v page
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