Journal of Operator Theory

Volume 58, Issue 1, Summer 2007 pp. 83-126.

Interpolation in the noncommutative Schur-Agler class

Authors: Joseph A. Ball (1) and Vladimir Bolotnikov (2)
Author institution: (1) Department of Mathematics, Virginia Polytechnic Institute, Blacksburg, VA 24061-0123, USA
(2) Department of Mathematics, The College of William and Mary, Williamsburg, VA 23187-8795, USA

Summary: The 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. There now has been introduced a noncommutative version of the Schur-Agler class which consists of formal power series in noncommuting indeterminates satisfying a noncommutative version of the von Neumann inequality when a tuple of operators (not necessarily commuting) coming from a noncommutative operator ball is plugged in for the formal indeterminates. The purpose of this paper is to extend the previously developed interpolation theory for the commutative Schur-Agler class to this noncommutative setting.

Keywords: Noncommutative Schur-Agler class, von Neumann inequality, formal power series in noncommutative indeterminates, conservative noncommutative structured multidimensional linear system, interpolation

Contents Full-Text PDF