Abstract
General results of interpolation (e.g., Nevanlinna-Pick) by elements in the noncommutative analytic Toeplitz algebraF ∞ (resp., noncommutative disc algebraA n) with consequences to the interpolation by bounded operator-valued analytic functions in the unit ball of ℂn are obtained. Noncommutative Poisson transforms are used to provide new von Neumann type inequalities. Completely isometric representations of the quotient algebraF ∞/J on Hilbert spaces whereJ is anyw *-closed, 2-sided ideal ofF ∞, are obtained and used to construct aw *-continuous,F ∞/J-functional calculus associated to row contractionsT=[T 1,…,T n] whenf(T1, …, Tn)=0 for anyf∈J. Other properties of the dual algebraF ∞/J are considered.
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