Some $K_0$-monoid properties preserved by tracial approximation

Abstract

We show that the following $K_0$-monoid properties of $C^*$-algebras in the class $\Omega$ are inherited by simple unital $C^*$-algebras in the class $TA\Omega$: \begin{enumerate} \item[(1)] almost divisible, \item[(2)] directly finite, \item[(3)] strong Riesz interpolation property. \end{enumerate}