Selfless reduced free products and graph products of $\mathrm{C}^\ast$-algebras

Abstract

Under mild assumptions, we show that reduced free products and reduced graph products of $\mathrm{C}^\ast$-algebras are selfless in the sense of L. Robert, without assuming the rapid decay property. In particular, our main theorems yield numerous new examples of simple, monotracial $\mathrm{C}^\ast$-algebras with strict comparison, stable rank one, and admitting a unique unital embedding of the Jiang-Su algebra $\mathcal{Z}$ up to approximate unitary equivalence.