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Free holomorphic functions and operator model theory (1111.5282v1)

Published 22 Nov 2011 in math.FA and math.OA

Abstract: This paper is an attempt to find large classes of noncommutative multivariable functions $g:\Omega\subset [B(\cH)n]_1-\to B(\cH)n$ for which a reasonable operator model theory and dilation theory can be developed for the noncommutative domain $g(\Omega)$. In other words, we want to transfer the free analogue of Nagy-Foias theory from the unit ball $[B(\cH)n]_1$ to other noncommutative domains, using appropriate maps.

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