Some (:*-algebras with outer

A condition is given viThich is both necessary and sufficient for every derivation of a separable C*-algebra to be inner (or, if there is no unit, to be determined by a multiplier). l. In [32] and [33], Sakai showed that every derivation of a simple C*-algebra is determined by a multiplier. In [2], it was shown that every derivation of a C*-algebra with continuous trace is determined by a multiplier (at least locally, and globally if there exists a suitable partition of unity on the spectrum, as there does if the spectrum is paracompact, and in particular if the C*-algebra is separable). While there are many other C*-algebras with the property that every derivation is determined by a multiplier notably, von Neumann algebras ([23], [31]; see also [2], [24] and [19]) , no separable C*-algebra other than a direct sum of simple and continuous trace C*-algebras has been shown to have this property. It is known that if A is a simple C*-algebra with unit such that every