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

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Abstract

Suppose \({\mathcal{T}_{+}(E)}\) 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 \({\mathcal{T}_{+}(E)}\) 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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Authors and Affiliations

  1. Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA

    Paul S. Muhly

  2. Department of Mathematics, Technion, 32000, Haifa, Israel

    Baruch Solel

Authors
  1. Paul S. Muhly
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  2. Baruch Solel
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Correspondence to Paul S. Muhly.

Additional information

The authors gratefully acknowledge support from the U.S.-Israel Binational Science Foundation. The second author gratefully acknowledges additional support from the Lowengart Research Fund.

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Muhly, P.S., Solel, B. Representations of Hardy Algebras: Absolute Continuity, Intertwiners, and Superharmonic Operators. Integr. Equ. Oper. Theory 70, 151–203 (2011). https://doi.org/10.1007/s00020-011-1869-0

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  • DOI: https://doi.org/10.1007/s00020-011-1869-0

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