Closed convex hulls of unitary orbits in certain simple real rank zero   C$^*$-algebras
  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. 
Ping Wong Ng and Paul Skoufranis
math.OA math.FA