On Automorphism Groups of Hardy Algebras

Published 17 Jun 2020 in math.OA | (2006.10184v1)

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