Closed convex hulls of unitary orbits in certain simple real rank zero C$^*$-algebras

TL;DR

This paper characterizes the convex hulls of unitary orbits of self-adjoint operators in certain simple real rank zero C*-algebras, providing new insights into their structure and approximation properties.

Contribution

It offers a complete description of these convex hulls and establishes bounds on the number of unitary conjugates needed for approximation.

Findings

Characterization of convex hull closures in specified C*-algebras

Upper bounds on unitary conjugates for approximations

Insights into the structure of self-adjoint operator orbits

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.