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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$C^ \ast$-extreme points of some compact $C^ \ast$-convex sets
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by D. R. Farenick and Phillip B. Morenz PDF
Proc. Amer. Math. Soc. 118 (1993), 765-775 Request permission

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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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 118 (1993), 765-775
  • MSC: Primary 46L05; Secondary 47A12, 47D20
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1139466-7
  • MathSciNet review: 1139466