November 22, 2004

Baruch Solel

Title: Non commutative Hardy algebras

Abstract:

The classical Hardy algebra $ H^{\infty}(\mathbb{T})$ can be viewed as an algebra of operators. (For instance, by viewing it as multiplication operators on $ H^2$.) In the litrature, various classes of operator algebras generalizing $ H^{\infty}$ have been studied. For example: analytic crossed products, free semigroup algebras, free semigroupoid algebras and quiver operator algebras. In the talk, I will present the class of Hardy algebras associated with correspondences. This class contains the previously mentioned classes of algebras.

Contractive representations of the classical Hardy algebra are given by (certain) contractions. One can view contractive representations of the non commutative Hardy algebras as "generalized contractions" and, as we shall see, this is a fruitful way of studying them.

I will discuss these representations, the associated notion of "duality" and some results illustrating the point made above. Most of the results are from a joint work with Paul Muhly.