Abstract
In this chapter it is shown that the set of all intertwining liftings with tolerance γ in the commutant lifting theorem is parameterized by a natural set of contractive analytic operator-valued functions. A Redheffer scattering interpolation of this parameterization is given. In the final three sections, state space formulas are given for the Redheffer scattering matrix parameterizing the set of all solutions for the standard left Nevanlinna-Pick, Nehari and two-block interpolation problems.
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© 1998 Springer Basel AG
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Foias, C., Frazho, A.E., Gohberg, I., Kaashoek, M.A. (1998). Parameterization of Intertwining Liftings and its Applications. In: Metric Constrained Interpolation, Commutant Lifting and Systems. Operator Theory Advances and Applications, vol 100. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8791-5_7
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DOI: https://doi.org/10.1007/978-3-0348-8791-5_7
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9775-4
Online ISBN: 978-3-0348-8791-5
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