Approximately inner flows

Abstract

When α is an approximately inner flow on a C * -algebra A and commutes with an automorphism γ of A we may extend α to a flow ᾱ on the crossed product A× γ Z by setting ᾱt (U ) = U where U is the canonical unitary implementing γ in A × γ Z and ask whether ᾱ is also approximately inner or not. We will consider very specific examples of this type; some of which we can answer affirmatively.