$C^*$-independence for $\mathbb{Z}_2$-graded $C^*$-algebras

Abstract

We analyse a notion of $C^*$-independence for $\mathbb{Z}_2$-graded $C^*$-algebras. We provide other notions of statistical independence for $\mathbb{Z}_2$-graded von Neumann algebras and prove some relationships between them. We provide a characterization for the graded nuclearity property.