Closed Convex Hulls of Unitary Orbits in Certain Simple Real Rank Zero C* -algebras. (1st October 2017)

• Record Type: Journal Article
• Authors: Ng, P.W.; Skoufranis, P.
• Is Part Of: Canadian journal of mathematics. Volume 69:Number 5(2017)
• Page Start: 1109
• Page End: 1142
• Publication Date: 2017-10-01
• Subjects: 46L05; convex hull of unitary orbits -- real rank zero C* -algebras simple -- eigenvalue function -- majorization; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/CJM-2016-045-5
• Languages: English
• ISSNs: 0008-414X

Abstract

Abstract: 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.