# Derivations Determined by Multipliers on Ideals of a C*-Algebra

### George A. Elliott

University of Copenhagen, Denmark

## Abstract

Sakai's theorem that every derivation of a simple C*-algebra is determined by a multiplier is generalized, in the class of separable approximately finite-dimensional C*-algebras, as follows. It is shown that, in such a C*-algebra, any derivation can be approximated arbitrarily closely in norm by a derivation which is determined by a multiplier on a nonzero closed two-sided ideal. It is shown, moreover, that the multiplier may be chosen to have norm bounded by fixed multiple of the norm of the derivation.

## Cite this article

George A. Elliott, Derivations Determined by Multipliers on Ideals of a C*-Algebra. Publ. Res. Inst. Math. Sci. 10 (1974), no. 3, pp. 721–728

DOI 10.2977/PRIMS/1195191888