Preprint
Schur Class Operator Functions and Automorphisms of Hardy Algebras
arXiv.org
Cornell University Library, arXiv.org
06/13/2007
DOI: 10.48550/arXiv.math/0606672
Abstract
Let \(E\) be a \(W^{\ast}\)-correspondence over a von Neumann algebra \(M\) and let \(H^{\infty}(E)\) be the associated Hardy algebra. If \(\sigma\) is a faithful normal representation of \(M\) on a Hilbert space \(H\), then one may form the dual correspondence \(E^{\sigma}\) and represent elements in \(H^{\infty}(E)\) as \(B(H)\)-valued functions on the unit ball \(\mathbb{D}(E^{\sigma})^{\ast}\). 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 M\"{o}bius transformations on \(\mathbb{D}(E^{\sigma})\). Particular attention is devoted to the \(H^{\infty}% \)-algebras that are associated to graphs.
Details
- Title: Subtitle
- Schur Class Operator Functions and Automorphisms of Hardy Algebras
- Creators
- Paul MuhlyBaruch Solel
- Resource Type
- Preprint
- Publication Details
- arXiv.org
- DOI
- 10.48550/arXiv.math/0606672
- eISSN
- 2331-8422
- Publisher
- Cornell University Library, arXiv.org; Ithaca
- Language
- English
- Date posted
- 06/13/2007
- Academic Unit
- Statistics and Actuarial Science; Mathematics
- Record Identifier
- 9984397948602771
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