Automorphisms determined by multipliers on ideals of a C∗-algebra

Various conditions on an automorphism of a C∗-algebra are shown to be equivalent in the case that the C∗-algebra is separable and approximately finite-dimensional. In a C∗-algebra every derivation of which is determined by a multiplier, and such that any hereditary sub-C∗-algebra also has this property (is this automatic?), all except the last of these conditions quickly reduce to saying that the restriction of the automorphism to some invariant essential closed two-sided ideal is determined by a multiplier.