Representations of logmodular algebras

Details Representations of logmodular algebras Representations of logmodular algebras

2008-06-02

arxiv.org/abs/0806.0284v2

Mathematics

Operator Algebras

14 pages, to appear in Trans. Amer. Math. Soc.

Scientific paper

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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