Weak Centrality: AF-algebras, C(X)-algebras, and group C*-algebras

We first prove that every AF-algebra is weakly central, thereby resolving a question left open by Archbold–Gogić. We then establish a new characterization of weak centrality for unital $C^{\ast }$-algebras in terms of $C(X)$-algebras. The paper concludes with an appendix that examines weak centrality in full group $C^{\ast }$-algebras and places these examples within the hierarchy of group classes.