We say that x is of the class C^{\infty} if there is a smooth mapping g\mapsto \alpha_g(x): G\rightarrow A where \alpha is an automorphism of the C*-algebra A and G is a Lie group. The tripple (A,G,\alpha) forms a C*-dynamical system. Define A^{\infty}:=\{x\in A: x~ \text{is of class }~ C^{\infty}\}. Show that A^{\infty} in dense in A.