Almost Homomorphisms Between Unital $C^*$-Algebras: A Fixed Point Approach (Analysis in Theory and Applications, 2011)
Let $A$, $B$ be two unital $C^*$−algebras. By using fixed point methods, we prove that every almost unital almost linear mapping $h : A → B$ which satisfies $h(2^nuy)= h(2^nu)h(y)$ for all $u \in U(A)$, all $y \in A$, and all $n=0,1,2, …$, is a homomorphism. Also, we establish the generalized Hyers–Ulam–Rassias stability of $*$−homomorphisms on unital $C^*$−algebras.