Osaka, H., Teruya, T. (2018). Permanence of nuclear dimension for inclusions of unital $C^*$-algebras with the Rokhlin property. Advances in Operator Theory, 3(1), 123-136. doi: 10.22034/aot.1703-1145

Hiroyuki Osaka; Tamotsu Teruya. "Permanence of nuclear dimension for inclusions of unital $C^*$-algebras with the Rokhlin property". Advances in Operator Theory, 3, 1, 2018, 123-136. doi: 10.22034/aot.1703-1145

Osaka, H., Teruya, T. (2018). 'Permanence of nuclear dimension for inclusions of unital $C^*$-algebras with the Rokhlin property', Advances in Operator Theory, 3(1), pp. 123-136. doi: 10.22034/aot.1703-1145

Osaka, H., Teruya, T. Permanence of nuclear dimension for inclusions of unital $C^*$-algebras with the Rokhlin property. Advances in Operator Theory, 2018; 3(1): 123-136. doi: 10.22034/aot.1703-1145

Permanence of nuclear dimension for inclusions of unital $C^*$-algebras with the Rokhlin property

Let $P \subset A$ be an inclusion of unital $C^*$-algebras and $E\colon A \rightarrow P$ be a faithful conditional expectation of index finite type. Suppose that $E$ has the Rokhlin property. Then $\dr(P) \leq \dr(A)$ and $\dim_{nuc}(P) \leq \dim_{nuc}(A)$. This can be applied to Rokhlin actions of finite groups. We also show that under the same above assumption if $A$ is exact and pure, that is, the Cuntz semigroups $W(A)$ has strict comparison and is almost divisible, then $P$ and the basic contruction $C^*\langle A, e_P\rangle$ are also pure.