Abstract
We obtain a noncommutative Nudel'man type interpolation theorem in several variables and a commutative analogue forH∞(Bn), the Hardy space of bounded analytic functions in the open ball of Cn. Using this result, we obtain an operatorial analogue in several variables of the Rosenblum–Rovnyak restriction theorem as well as an extension to the noncommutative analytic Toeplitz algebraF∞. We provide new extensions of the Carathéodory–Fejér and Nevanlinna–Pick interpolation theorems forF∞.
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