Lie $^*$-double derivations on Lie $C^*$-algebras | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 8، دوره 1، شماره 2، 2010، صفحه 63-71 اصل مقاله (205.69 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2010.76 | ||
| نویسنده | ||
| N. Ghobadipour* | ||
| Department of Mathematics, Urmia University, Urmia, Iran. | ||
| چکیده | ||
| A unital $C^*$-algebra $\mathcal{A}$ endowed with the Lie product $[x,y]=xy- yx$ on $\mathcal{A}$ is called a Lie $C^*$-algebra. Let $\mathcal{A}$ be a Lie $C^*$-algebra and $g,h:\mathcal{A}\to \mathcal{A}$ be $\mathbb{C}$-linear mappings. A $\mathbb{C}$-linear mapping $f:\mathcal{A}\to \mathcal{A}$ is called a Lie $(g,h)$--double derivation if $f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all $a,b\in \mathcal{A}$. In this paper, our main purpose is to prove the generalized Hyers–Ulam–Rassias stability of Lie $*$-double derivations on Lie $C^*$-algebras associated with the following additive mapping: $$ \sum^{n}_{k=2}(\sum^{k}_{i_{1}=2} \sum^{k+1}_{i_{2}=i_{1}+1}... \sum^{n}_{i_{n-k+1}=i_{n-k}+1}) f(\sum^{n}_{i=1, i\neq i_{1},..,i_{n-k+1} } x_{i}-\sum^{n-k+1}_{ r=1}x_{i_{r}})+f(\sum^{n}_{ i=1} x_{i}) =2^{n-1} f(x_{1}) $$ for a fixed positive integer $n$ with $n \geq 2.$ | ||
| کلیدواژهها | ||
| Generalized Hyers-Ulam-Rassias stability؛ $*$-double derivation؛ Lie $C^*$-algebra | ||
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