arXiv 0812.29332008-12-15math.OA

$C^*$ -三元代数中同态和导子的稳定性

Stability of homomorphisms and derivations in $C^*$-ternary algebras

M. Bavand Savadkouhi, M. Eshaghi Gordji, N. Ghobadipour

摘要：

本文研究了$C^*$ -三元代数与$C^*$ -三元代数上的导子之间的同态，并结合下面的函数方程$$f(\frac{x_2-x_1}{3})+f(\frac{x_1-3x_3}{3})+f(\frac{3x_1+3x_3-x_2}{3})=f(x_1).$$证明了$C^*$ -三元代数上的同态和$C^*$-三元代数上的导子的广义Hyers-Ulam -Rassias稳定性.

英文摘要：

In this paper, we investigate homomorphisms between $C^*$-ternary algebras and derivations on $C^*$-ternary algebras, associated with the following functional equation $$f(\frac{x_2-x_1}{3})+f(\frac{x_1-3x_3}{3})+f(\frac{3x_1+3x_3-x_2}{3})=f(x_1).$$ Moreover, we prove the generalized Hyers-Ulam -Rassias stability of homomorphisms in $C^*$-ternary algebras and of derivations on $C^*$-ternary algebras.

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