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Representations of logmodular algebras
Author(s):
Vern
I.
Paulsen;
Mrinal
Raghupathi
Journal:
Trans. Amer. Math. Soc.
363
(2011),
2627-2640.
MSC (2010):
Primary 47L55;
Secondary 47A67, 47A20
Posted:
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  -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:
10.1090/S0002-9947-2010-05151-7
PII:
S 0002-9947(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
Posted:
December 28, 2010
Additional Notes:
This research was supported in part by NSF grant DMS-0600191.
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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