INNER DERIVATIONS ON SIGMA-C-ASTERISK-ALGEBRAS

We prove the following two improvements of a result of BECKER. (1) If A is a pro-C-algebra, then every derivation on A is approximately inn er. (2) If A is a separable sigma-C-algebra, and if every C* quotient of A has the property that every derivation on it is inner, then also every derivation on A is inner.We also give an example of a derivatio n on a separable sigma-C-algebra which is not inner but which induces an inner derivation on every C quotient.