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Schur class operator functions and automorphisms of Hardy algebras
Journal article   Open access   Peer reviewed

Schur class operator functions and automorphisms of Hardy algebras

Paul S. Muhly and Baruch Solel
Documenta mathematica Journal der Deutschen Mathematiker-Vereinigung, Vol.13, pp.365-411
01/01/2008
DOI: 10.4171/dm/250
url
https://doi.org/10.4171/dm/250View
Published (Version of record) Open Access

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.
Mathematics Physical Sciences Science & Technology

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