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Representations of logmodular algebras


Authors: Vern I. Paulsen and Mrinal Raghupathi
Journal: Trans. Amer. Math. Soc. 363 (2011), 2627-2640
MSC (2010): Primary 47L55; Secondary 47A67, 47A20
DOI: https://doi.org/10.1090/S0002-9947-2010-05151-7
Published electronically: December 28, 2010
MathSciNet review: 2763729
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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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Additional Information

Vern I. Paulsen
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204
Email: vern@math.uh.edu

Mrinal Raghupathi
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
Email: mrinal.raghupathi@vanderbilt.edu

DOI: https://doi.org/10.1090/S0002-9947-2010-05151-7
Keywords: Logmodular algebra, completely contractive, 2-summing, semispectral
Received by editor(s): June 2, 2008
Received by editor(s) in revised form: June 30, 2009
Published electronically: December 28, 2010
Additional Notes: This research was supported in part by NSF grant DMS-0600191.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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