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)
  • Received : 2009.09.25
  • Accepted : 2010.01.18
  • Published : 2010.03.30

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

References

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