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

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.,...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2009-07, Vol.137 (7), p.2311-2315
Main Author: Walter, Martin E.
Format: Article
Language:English
Subjects:
Algebra
Coefficients
Commutative rings and algebras
Convex and discrete geometry
Exact sciences and technology
Functional analysis
General mathematics
General, history and biography
Geometry
Inner products
Mathematical analysis
Mathematics
Matrices
Operator algebras
Sciences and techniques of general use
Semicircles
Sine function
Tangents
Von Neumann algebra
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-09-09868-2