We study algebras of bounded, noncommutative (nc) analytic functions on nc subvarieties of
the nc unit ball. Given an nc variety $\mathfrak {V} $ in the nc unit ball $\mathfrak {B} _d …

This is an extended version of a three part mini course on the Drury–Arveson space given as
part of the Focus Program on Analytic Function Spaces and their Applications, hosted by the …

We study reproducing kernel Hilbert spaces on the unit ball with the complete Nevanlinna–
Pick property through the representation theory of their algebras of multipliers. We give a …

The Drury-Arveson space $ H^ 2_d $, also known as symmetric Fock space or the $ d $-shift
space, is a Hilbert function space that has a natural $ d $-tuple of operators acting on it …

We continue the investigation of the isomorphism problem for multiplier algebras of
reproducing kernel Hilbert spaces with the complete Nevanlinna-Pick property. In contrast to …

We study the isomorphism problem for the multiplier algebras of irreducible complete Pick
kernels. These are precisely the restrictions $\mathcal {M} _V $ of the multiplier algebra …

We study crossed products of arbitrary operator algebras by locally compact groups of
completely isometric automorphisms. We develop an abstract theory that allows for …

Semicrossed product algebras have been used to study dynamical systems since their
introduction by Arveson in 1967. In this survey article, we discuss the history and some …

Given a noncommutative (nc) variety V in the nc unit ball B d, we consider the algebra
H∞(V) of bounded nc holomorphic functions on V. We investigate the problem of when two …

These notes are the output of a decade of research on how the results about dilations of one-
parameter CP-semigroups with the help of product systems, can be put forward to d …