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arXiv · 0806.0284

Representations of logmodular algebras

Vern I. Paulsen·Mrinal Raghupathi
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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 semispectral measures. We establish some matrix factorization results for uniform logmodular algebras

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Vern I. Paulsen, Mrinal Raghupathi. 2008-06-02. Representations of logmodular algebras. https://arxiv.org/abs/0806.0284

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