Schur Class Operator Functions and Automorphisms of Hardy Algebras
| dc.creator | Muhly, Paul S. | |
| dc.creator | Solel, Baruch | |
| dc.date | 2006-06-27 | |
| dc.date | 2007-06-13 | |
| dc.date.accessioned | 2026-07-07T08:07:58Z | |
| dc.date.available | 2026-07-07T08:07:58Z | |
| dc.description | Let $E$ be a $W^{\ast}$-correspondence over a von Neumann algebra $M$ and let $H^{\infty}(E)$ be the associated Hardy algebra. If $σ$ is a faithful normal representation of $M$ on a Hilbert space $H$, then one may form the dual correspondence $E^σ$ and represent elements in $H^{\infty}(E)$ as $B(H)$-valued functions on the unit ball $\mathbb{D}(E^σ)^{\ast}$. The functions that one obtains are called Schur class functions and may be characterized in terms of certain Pick-like kernels. We study these functions and relate them to system matrices and transfer functions from systems theory. We use the information gained to describe the automorphism group of $H^{\infty}(E)$ in terms of special Möbius transformations on $\mathbb{D}(E^σ)$. Particular attention is devoted to the $H^{\infty}% $-algebras that are associated to graphs. | |
| dc.description | Minor corrections. A few comments and references added | |
| dc.identifier | https://arxiv.org/abs/math/0606672 | |
| dc.identifier | http://arxiv.org/abs/math/0606672 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131107 | |
| dc.subject | Operator Algebras | |
| dc.subject | 47A57, 47L55, 47L65, 47L75, 46L08, 46L53, 47A48, 46L52, 47L30, 46T25 | |
| dc.title | Schur Class Operator Functions and Automorphisms of Hardy Algebras | |
| dc.type | text |