In this book the authors develop a theory of free noncommutative functions, in both algebraic
and analytic settings. Such functions are defined as mappings from square matrices of all …

Abstract The Schur–Agler class consists of functions over a domain satisfying an appropriate
von Neumann inequality. Originally defined over the polydisk, the idea has been extended …

There are three new things in this paper about the open symmetrized bidisk G={(z 1+ z 2, z 1
z 2):| z 1|,| z 2|< 1}. They are, in the order in which they will be proved,(1) The Realization …

A set Ω is a spectral set for an operator T if the spectrum of T is contained in Ω, and von
Neumann's inequality holds for T with respect to the algebra R (Ω) of rational functions with …

We prove a realization formula and a model formula for analytic functions with modulus
bounded by 1 on the symmetrized bidisc G= def {(z+ w, zw):| z|< 1,| w|< 1}. As an application …

A seminal result of Agler characterizes the so-called Schur-Agler class of functions on the
polydisk in terms of a unitary colligation transfer function representation. We generalize this …

Given a collection of test functions, one defines the associated Schur–Agler class as the
intersection of the contractive multipliers over the collection of all positive kernels for which …

It is well known that unital contractive representations of the disk algebra are completely
contractive. Let A denote the subalgebra of the disk algebra consisting of those functions f …

We give a set of test functions for $ H_ {1}^{\infty} $, the algebra of bounded holomorphic
functions on the disk with first derivative equal to $0 $, whose interpolation problem was …

We identify the set of extreme points and apply Choquet theory to a normalized matrix-
measure ball subject to finitely many linear side constraints. As an application we obtain …