2016/08/15 by Ng, Ping Wong, Robert, Leonel, Skoufranis, Paul
#FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1608.04350
We investigate the closed convex hull of unitary orbits of selfadjoint elements in arbitrary unital C*-algebras. Using a notion of majorization against unbounded traces, a characterization of these closed convex hulls is obtained. Furthermore, for C*-algebras satisfying Blackadar's strict comparison of positive elements by traces or for collections of C*-algebras with a uniform bound on their nuclear dimension, an upper bound for the number of unitary conjugates in a convex combination required to approximate an element in the closed convex hull within a given error is shown to exist. This property, however, fails for certain "badly behaved" simple nuclear C*-algebras.