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

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

2010-06-08

arxiv.org/abs/1006.1398v1

Mathematics

Operator Algebras

Scientific paper

Suppose $\mathcal{T}_{+}(E)$ is the tensor algebra of a $W^{*}$-correspondence $E$ and $H^{\infty}(E)$ is the associated Hardy algebra. We investigate the problem of extending completely contractive representations of $\mathcal{T}_{+}(E)$ on a Hilbert space to ultra-weakly continuous completely contractive representations of $H^{\infty}(E)$ on the same Hilbert space. Our work extends the classical Sz.-Nagy - Foia\c{s} 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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