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

Walter, Martin

doi:10.1090/S0002-9939-09-09868-2

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.

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