JournalsprimsVol. 10, No. 3pp. 721–728

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

  • George A. Elliott

    University of Copenhagen, Denmark
Derivations Determined by Multipliers on Ideals of a C*-Algebra cover
Download PDF

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