Representations of logmodular algebras

Paulsen, Vern; Raghupathi, Mrinal

doi:10.1090/S0002-9947-2010-05151-7

Representations of logmodular algebras
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by Vern I. Paulsen and Mrinal Raghupathi

Trans. Amer. Math. Soc. 363 (2011), 2627-2640

DOI: https://doi.org/10.1090/S0002-9947-2010-05151-7

Published electronically: December 28, 2010

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Abstract:

We study the question of whether or not contractive representations of logmodular algebras are completely contractive. We prove that a 2-contractive representation of a logmodular algebra extends to a positive map on the enveloping $C^*$-algebra, which we show generalizes a result of Foias and Suciu on uniform logmodular algebras. Our proof uses non-commutative operator space generalizations of classical results on 2-summing maps and semi-spectral measures. We establish some matrix factorization results for uniform logmodular algebras.

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