An abstract analogon of the de Branges-Rovnyak functional model

Given a Hilbert spaceK generated by two of its subspaces,K=K₁K₂, we investigate the representation ofK inK₁K₂ which assigns to eachk K the pairPk=P(K₁)k P(K₂)k consisting of its orthogonal projections ontoK₁ andK₂.A part of this work was done during the visit of the second author at the University of Sevilla, Spain in September-October 1989. The support of Junta Andalusia is gratefully aknowledged.