TY - JOUR
T1 - Almost Homomorphisms Between Unital $C^*$-Algebras: A Fixed Point Approach
JO - Analysis in Theory and Applications
VL - 4
SP - 320
EP - 331
PY - 2011
DA - 2011/11
SN - 27
DO - http://doi.org/10.1007/s10496-011-0320-3
UR - https://global-sci.org/intro/article_detail/ata/4604.html
KW - alternative fixed point, Jordan $*$-homomorphism.
AB - <p style="text-align: justify;">Let $A$, $B$ be two unital $C^*$−algebras. By using fixed point methods, we prove that every almost unital almost linear mapping $h : A \to B$ which satisfies $h(2^nuy)= h(2^nu)h(y)$ for all $u \in U(A)$, all $y \in A$, and all $n=0,1,2, \cdots$, is a homomorphism. Also, we establish the generalized Hyers–Ulam–Rassias stability of $*$−homomorphisms on unital $C^*$−algebras.</p>