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# Closed Convex Hulls of Unitary Orbits in Certain Simple Real Rank Zero C$^*$-algebras

Published:2017-02-16
Printed: Oct 2017
• P. W. Ng,
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana, USA, 70504-3568
• P. Skoufranis,
Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada, M3J 1P3
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## Abstract

In this paper, we characterize the closures of convex hulls of unitary orbits of self-adjoint operators in unital, separable, simple C$^*$-algebras with non-trivial tracial simplex, real rank zero, stable rank one, and strict comparison of projections with respect to tracial states. In addition, an upper bound for the number of unitary conjugates in a convex combination needed to approximate a self-adjoint are obtained.
 Keywords: convex hull of unitary orbits, real rank zero C*-algebras simple, eigenvalue function, majorization
 MSC Classifications: 46L05 - General theory of $C^*$-algebras

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