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. 721–728DOI 10.2977/PRIMS/1195191888