Noncommutative Geometry

Abstract: Nevanlinna-Pick spaces are Hilbert function spaces which mirror some of the fine structure of the classical Hardy space on the unit disc.

Their multiplier algebras are an important class of non self-adjoint operator algebras of functions. I will talk about recent work with Raphael Clouatre, in which we investigate representations of these multiplier algebras. In particular, we determine the boundary representations in the sense of Arveson of a special class of multiplier algebras. As a consequence, we find that these algebras, despite being commutative, can only be embedded into non-commutative C*-algebras.