Kishimoto's Conjugacy Theorems in Simple C*-Algebras of Tracial Rank One

摘要

Let A be a unital separable simple amenable C*-algebra with finite tracial rank which satisfies the Universal Coefficient Theorem. Suppose alpha and beta are two automorphisms with the Rokhlin property that induce the same action on the K-theoretical data of A. We show that alpha and beta are strongly outer conjugate and uniformly approximately conjugate, that is, there exists a sequence of unitaries {u(n)} subset of A and a sequence of strongly asymptotically inner automorphisms sigma(n) such that