Interpolation in the noncommutative Schur-Agler class

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dc.creatorBall, Joseph A.
dc.creatorBolotnikov, Vladimir
dc.date2005-06-26
dc.date.accessioned2026-07-07T05:21:09Z
dc.date.available2026-07-07T05:21:09Z
dc.descriptionThe class of Schur-Agler functions over a domain ${\mathcal D} \subset {\mathbb C}^{d}$ is defined as the class of holomorphic operator-valued functions on ${\mathcal D}$ for which a certain von Neumann inequality is satisfied when a commuting tuple of operators satisfying a certain polynomial norm inequality is plugged in for the variables. Such functions are alternatively characterized as those having a linear-fractional presentation which identifies them as transfer functions of a certain type of conservative structured multidimensional linear system. There now has been introduced a noncommutative version of the Schur-Agler class which consists of formal power series in noncommuting indeterminants satisfying a noncommutative version of the von Neumann inequality when a tuple of operators (not necessarily commuting) coming from a noncommutative operator ball are plugged in for the formal indeterminants. Formal power series in this noncommutative Schur-Agler class in turn are characterized as those having a certain linear-fractional presentation in noncommuting variables identifying them as transfer functions of a recently introduced class of conservative structure multidimensional linear systems having evolution along a free semigroup rather than along an integer lattice. The purpose of this paper is to extend the previously developed interpolation theory for the commutative Schur-Agler class to this noncommutative setting.
dc.identifierhttps://arxiv.org/abs/math/0506532
dc.identifierhttp://arxiv.org/abs/math/0506532
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75590
dc.subjectFunctional Analysis
dc.titleInterpolation in the noncommutative Schur-Agler class
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