Representations of logmodular algebras
Operator Algebras
2010-03-24 v2 Functional Analysis
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
Cite
@article{arxiv.0806.0284,
title = {Representations of logmodular algebras},
author = {Vern I. Paulsen and Mrinal Raghupathi},
journal= {arXiv preprint arXiv:0806.0284},
year = {2010}
}
Comments
14 pages, to appear in Trans. Amer. Math. Soc.