Geodesic
Derivations on some (possibly non-separable) C*-algebras
Glasgow mathematical journal, Tome 22 (1981) no. 1, pp. 43-56

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In an important recent paper [4], G. A. Elliott has given a necessary and sufficient condition for every derivation on a separable C*-algebra with identity to be inner. Indeed, Elliott's condition has since been shown, by Akemann and Pedersen, to be equivalent to the C*-algebra being a finite direct sum of C*-algebras which are either homogeneous of finite degree or simple [8, Corollary 3.10]. 
Sproston, J. P. Derivations on some (possibly non-separable) C*-algebras. Glasgow mathematical journal, Tome 22 (1981) no. 1, pp. 43-56. doi: 10.1017/S0017089500004456
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