Off-diagonal matrix coefficients are tangents to state space: Orientation and C*-algebras
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- by Martin E. Walter PDF
- Proc. Amer. Math. Soc. 137 (2009), 2311-2315 Request permission
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.References
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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
- Received by editor(s): May 2, 2008
- Published electronically: February 18, 2009
- Communicated by: Marius Junge
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2311-2315
- MSC (2000): Primary 46L30, 46L05; Secondary 43A30
- DOI: https://doi.org/10.1090/S0002-9939-09-09868-2
- MathSciNet review: 2495264