APPROXIMATELY INNER σ− DYNAMICS ON C∗− ALGEBRAS

Let D be a ∗− subalgebra of C∗− algebra A and σ : D → A be a linear operator. In this paper we introduce the notions of (approximately inner) σ− derivations and (approximately inner) σ− dynamics on C∗− algebras and present several results concerning on the approximately innerness of such dynamics. In particular we prove that if {ϕt}t∈R is a σ− dynamics on the C∗− algebra A satisfying I ϕt I≤ 2 I σ I +1 and there exists a core D0 for the generator d of {ϕt}t∈R such that d (as a σ− derivation) is approximately inner on D0, then {ϕt}t∈R is an approximately inner σ− dynamics.