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

$ C\sp \ast$-extreme points of some compact $ C\sp \ast$-convex sets


Authors: D. R. Farenick and Phillip B. Morenz
Journal: Proc. Amer. Math. Soc. 118 (1993), 765-775
MSC: Primary 46L05; Secondary 47A12, 47D20
MathSciNet review: 1139466
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Abstract: In the $ {C^{\ast}}$-algebra $ {M_n}$ of complex $ n \times n$ matrices, we consider the notion of noncommutative convexity called $ {C^{\ast}}$-convexity and the corresponding notion of a $ {C^{\ast}}$-extreme point. We prove that each irreducible element of $ {M_n}$ is a $ {C^{\ast}}$-extreme point of the $ {C^{\ast}}$-convex set it generates, and we classify the $ {C^{\ast}}$-extreme points of any $ {C^{\ast}}$-convex set generated by a compact set of normal matrices.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1139466-7
PII: S 0002-9939(1993)1139466-7
Keywords: Matricial range, $ {C^{\ast}}$-convex set, $ {C^{\ast}}$-extreme point
Article copyright: © Copyright 1993 American Mathematical Society