LINEAR*-DERIVATIONS ON C*-ALGEBRAS

Abstract

It is shown that for a derivation ｆ(χ1 ··· χｊ-1χｊχｊ+1 ··· χk) = k∑ｊ=1 χ1 ··· χｊ-1χｊ+1 ···χkｆ(χｊ) on a unital C*-algebra Β, there exists a unique Ｃ-linear *-derivation Ｄ: Β→Β near the derivation, by using the Hyers-Ulam-Rassias stability of functional equations. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297--300.