Journal article
Schur class operator functions and automorphisms of Hardy algebras
Documenta mathematica Journal der Deutschen Mathematiker-Vereinigung, Vol.13, pp.365-411
01/01/2008
DOI: 10.4171/dm/250
Abstract
Let E be a W*-correspondence over a von Neumann algebra M and let H(infinity) (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(infinity) (E) as B(H)-valued functions on the unit ball D(E(sigma))*. 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 related them to system matrices and transfer functions from systems theory. We use the information gained to describe the automorphism group of H(infinity) (E) in terms of special Mobius transformations on D(E(sigma)). Particular attention is devoted to the H(infinity)-algebras that are associated to graphs.
Details
- Title: Subtitle
- Schur class operator functions and automorphisms of Hardy algebras
- Creators
- Paul S. Muhly - Univ Iowa, Dept Math, Iowa City, IA 52242 USABaruch Solel - Technion – Israel Institute of Technology
- Resource Type
- Journal article
- Publication Details
- Documenta mathematica Journal der Deutschen Mathematiker-Vereinigung, Vol.13, pp.365-411
- DOI
- 10.4171/dm/250
- ISSN
- 1431-0643
- eISSN
- 1431-0643
- Publisher
- UNIV BIELEFELD
- Number of pages
- 47
- Language
- English
- Date published
- 01/01/2008
- Academic Unit
- Statistics and Actuarial Science; Mathematics
- Record Identifier
- 9984398375902771
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