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

Published online by Cambridge University Press:  20 November 2018

P.W. Ng  and
P. Skoufranis
P.W. Ng
Affiliation:
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana, USA, 70504-3568 e-mail: png@louisiana.edu
P. Skoufranis
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3 e-mail: pskoufra@yorku.ca
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Abstract

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In this paper, we characterize the closures of convex hulls of unitary orbits of self-adjoint operators in unital, separable, simple ${{\text{C}}^{*}}$ -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

46L05convex hull of unitary orbitsreal rank zero C* -algebras simpleeigenvalue functionmajorization
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 69 , Issue 5 , 01 October 2017 , pp. 1109 - 1142
Copyright
Copyright © Canadian Mathematical Society 2017

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