Centrally Large Subalgebras and Tracial $\mathcal{Z}$-Absorption

Abstract

Let $A$ be a simple infinite dimensional stably finite unital C*-algebra, and let $B$ be a centrally large subalgebra of $A$. We prove that if $A$ is tracially $\mathcal{Z}$-absorbing if and only if $B$ is tracially $\mathcal{Z}$-absorbing. If $A$ and $B$ are also separable and nuclear, we prove that $A$ is $\mathcal{Z}$-absorbing if and only if $B$ is $\mathcal{Z}$-absorbing.

15 pages

References in corpus (1)

• Completely positive maps of order zero