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LINEAR *-DERIVATIONS ON C*-ALGEBRAS  

Park, Choonkil (Department of Mathematics Research Institute for Natural Sciences Hanyang University)
Lee, Jung Rye (Department of Mathematics Daejin University)
Lee, Sung Jin (Department of Mathematics Daejin University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.23, no.1, 2010 , pp. 49-57 More about this Journal
Abstract
It is shown that for a derivation $$f(x_1{\cdots}x_{j-1}x_jx_{j+1}{\cdots}x_k)=\sum_{j=1}^{k}x_{1}{\cdots}x_{j-1}x_{j+1}{\cdots}x_kf(x_j)$$ on a unital $C^*$-algebra $\mathcal{B}$, there exists a unique $\mathbb{C}$-linear *-derivation $D:{\mathcal{B}}{\rightarrow}{\mathcal{B}}$ 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.
Keywords
linear *-derivation; $C^*$-algebra; functional equation; Hyers-Ulam-Rassias stability;
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