Raphael Clouatre, Department of Pure Mathematics, University of Waterloo
“Classification of C0 contractions and boundary representations”
The classical Sz.-Nagy–Foias model theory for Hilbert space contractions represents (up to unitary equivalence) any completely non-unitary contraction as a concrete operator on a Hilbert space valued function space. As such, the model operator is very complicated. There is a simpler classification theory associated to a smaller class of operators, called the class C0. The model here acts on a direct sum of scalar valued Hardy spaces, but it only represents contractions up to quasisimilarity.
We will be looking at the problem of improving this relation of quasisimilarity to unitary equivalence through the study of some natural non self-adjoint operator algebras and their boundary representations. We will also mention a potential refinement of Paulsen’s theorem on completely bounded homomorphisms and its connection with the problem of classification up to similarity.