Central Intertwining Lifting, Suboptimization, and Interpolation in Several Variables

In this paper we obtain an explicit central intertwining lifting for row contractions. This is used to prove Kaftal–Larson–Weiss and Foiaş–Frazho H∞−H2 suboptimization type results for the noncommutative (resp. commutative) analytic Toeplitz algebra F∞n (resp. W∞n). The algebra F∞n (resp. W∞n) can be viewed as a multivariable noncommutative (resp. commutative) analogue of the Hardy space H∞. Similar results are provided for F∞n⊗B(K, K′) and W∞n⊗B(K, K′), where B(K, K′) is the set of all bounded linear operators acting on Hilbert spaces. New extensions of the Sarason, Carathéodory, and Nevanlinna–Pick type interpolation results are obtained for F∞n⊗B(K, K′) and some consequences to the operator-valued analytic interpolation in the unit ball of Cn are considered.