On Automorphism Groups of Hardy Algebras

Abstract

Let $E$ be a $W^{\ast }$-correspondence and let $H^{\infty }(E)$ be the associated Hardy algebra. The unit disc of intertwiners $\mathbb{D}((E^{\sigma }{)}^{\ast })$ plays a central role in the study of $H^{\infty }(E)$. We show a number of results related to the automorphism groups of both $H^{\infty }(E)$ and $\mathbb{D}((E^{\sigma }{)}^{\ast })$. We find a matrix representation for these groups and describe several features of their algebraic structure. Furthermore, we show an application of $Aut(\mathbb{D}((E^{\sigma }{)}^{\ast }))$ to the study of Morita equivalence of $W^{\ast }$-correspondences.

References in corpus (3)

• Proper Analytic Free Maps
• Morita Transforms of Tensor Algebras
• Morita Equivalence of W*-Correspondences and their Hardy Algebras