Geodesic
Schur class operator functions and automorphisms of Hardy algebras
Documenta mathematica, Tome 13 (2008), pp. 365-411
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Let E be a W∗-correspondence over a von Neumann algebra M and let H∞(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 Eσ and represent elements in H∞(E) as B(H)-valued functions on the unit ball D(Eσ)∗. 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∞(E) in terms of special Möbius transformations on D(Eσ). Particular attention is devoted to the H∞-algebras that are associated to graphs.
DOI : 10.4171/dm/250
Classification : 46E22, 46E50, 46G20, 46H15, 46H25, 46K50, 46L08, 46L89
Mots-clés : graph algebras, Hardy algebras, tensor algebras, Schur class functions, W∗-correspondence, noncommutative realization theory, Möbius transformations, free semigroup algebras, Nevanlinna-Pick interpolation 
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     author = {Baruch Solel and Paul S. Muhly},
     title = {Schur class operator functions and automorphisms of {Hardy} algebras},
     journal = {Documenta mathematica},
     pages = {365--411},
     year = {2008},
     volume = {13},
     doi = {10.4171/dm/250},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/250/}
}
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Baruch Solel; Paul S. Muhly. Schur class operator functions and automorphisms of Hardy algebras. Documenta mathematica, Tome 13 (2008), pp. 365-411. doi: 10.4171/dm/250

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