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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Off-diagonal matrix coefficients are tangents to state space: Orientation and C*-algebras


Author: Martin E. Walter
Journal: Proc. Amer. Math. Soc. 137 (2009), 2311-2315
MSC (2000): Primary 46L30, 46L05; Secondary 43A30
Published electronically: February 18, 2009
MathSciNet review: 2495264
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Abstract: Any non-commutative C*-algebra $ \mathcal{A}$, e.g., two by two complex matrices, has at least two associative multiplications for which the collection of positive linear functionals is the same. Alfsen and Shultz have shown that by selecting an orientation for the state space $ K$ of $ \mathcal{A}$, i.e., the convex set of positive linear functionals of norm one, a unique associative multiplication for $ \mathcal{A}$ is determined. We give a simple method for describing this orientation.


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Additional Information

Martin E. Walter
Affiliation: Department of Mathematics, University of Colorado, Campus Box 395, Boulder, Colorado 80309
Email: walter@euclid.colorado.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09868-2
PII: S 0002-9939(09)09868-2
Keywords: C*-algebra, positive linear functional, state space, matrix coefficient, orientation
Received by editor(s): May 2, 2008
Published electronically: February 18, 2009
Communicated by: Marius Junge
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.