Let A be a simple unital C∗-algebra with tracial rank zero and with a unique tracial state and let Φ be an involutory ∗-antiautomorphism of A. It is shown that the associated real algebra AΦ = {a ∈ A : Φ(a) = a∗} also has tracial rank zero. Let A be a unital simple separable C∗-algebra with tracial rank zero and suppose that A has a unique tracial state. If Φ is an involutory ∗-antiautomorphism...

We investigate connections between actions on separable C?-algebras with Rokhlin-type properties and absorption of the Jiang-Su algebra Z. show that if A admits an approximately inner group action finite Rokhlin dimension commuting towers then is Z-stable. obtain analogous results for tracial version property approximate innerness. Going beyond innerness, a single automorphism which have are al...

‎Let $Omega$ be a class of unital‎ ‎$C^*$-algebras‎. ‎We introduce the notion of a local tracial $Omega$-algebra‎. ‎Let $A$ be an $alpha$-simple unital local tracial $Omega$-algebra‎. ‎Suppose that $alpha:Gto $Aut($A$) is an action of a finite group $G$ on $A$‎ ‎which has a certain non-simple tracial Rokhlin property‎. ‎Then the crossed product algebra‎ ‎$C^*(G,A,alpha)$ is a unital local traci...

Abstract Let G be a finite group, let A an infinite-dimensional stably simple unital C*-algebra, and $\alpha \colon \to {\operatorname {Aut}} (A)$ action of on which has the weak tracial Rokhlin property. $A^{\alpha }$ fixed point algebra. Then radius comparison satisfies ${\operatorname {rc}} (A^{\alpha }) \leq ( C^* (G, A, \alpha ) ({1}/{{{\operatorname{card}}} (G))} \cdot . The inclusion in ...