Representations of Hardy Algebras: Absolute Continuity, Intertwiners and Superharmonic Operators

2010/06/08 by Paul S. Muhly, Muhly, Paul S., Baruch Solel +1
Mathematics · #46L08 #46L52 #46L89 #47L30 #47L55 #47L65 #47L75 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L08 #msc:46L52 #msc:46L89 #msc:47L30 #msc:47L55 #msc:47L65 #msc:47L75

paper · pdf · doi:10.48550/arxiv.1006.1398

arxiv created 2010/06/08 · arxiv updated 2010/06/09

Abstract

Suppose T₊(E) is the tensor algebra of a W^*-correspondence E and H^∞(E) is the associated Hardy algebra. We investigate the problem of extending completely contractive representations of T₊(E) on a Hilbert space to ultra-weakly continuous completely contractive representations of H^∞(E) on the same Hilbert space. Our work extends the classical Sz.-Nagy - Foiaş functional calculus and more recent work by Davidson, Li and Pitts on the representation theory of Popescu's noncommutative disc algebra.

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