Proceedings of the American Mathematical Society

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

Author(s): Martin E. Walter
Journal: Proc. Amer. Math. Soc. 137 (2009), 2311-2315.
MSC (2000): Primary 46L30, 46L05; Secondary 43A30
Posted: February 18, 2009
Retrieve article in: PDF

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

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.

1.: Alfsen, Erik M., and Shultz, Frederic W., State Spaces of Operator Algebras: Basic Theory, Orientations, and C*-Products, Birkhäuser, Boston, MA, 2001. MR 1828331 (2002h:46100)
2.: Alfsen, Erik M., and Shultz, Frederic W., Geometry of State Spaces of Operator Algebras, Birkhäuser, Boston, MA, 2003. MR 1947002 (2004b:46088)
3.: Cohen, Robert A., and Walter, Martin E., An Explicit Duality for Finite Groups. Operator Theory, Operator Algebras, and Applications, Contemporary Mathematics 414, Han, D., Jorgensen, P.E.T., Larson, D.R., Editors, Amer. Math. Soc., Providence, RI, 2006, pp. 87-96. MR 2277205 (2008m:43005)
4.: Walter, Martin E., Algebraic Structures Determined by 3 by 3 Matrix Geometry, Proc. Amer. Math. Soc., 131:2129-2131, 2003. MR 1963763 (2004c:46137)
5.: Walter, Martin E., Differentiation on the Dual of a Group: An Introduction, Rocky Mountain Journal of Mathematics, 12(3): 497-536, 1982. MR 672234 (84g:22018)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46L30, 46L05, 43A30

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

DOI: 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
Posted: February 18, 2009
Communicated by: Marius Junge
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS