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arXiv · 2006.10184

On Automorphism Groups of Hardy Algebras

Rene Ardila
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Abstract

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

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Rene Ardila. 2020-06-17. On Automorphism Groups of Hardy Algebras. https://doi.org/10.1007/s43034-020-00079-5

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