Jordan $*$-homomorphisms between unital $C^*$-algebras
Commun. Korean Math. Soc. 2012 Vol. 27, No. 1, 149-158
https://doi.org/10.4134/CKMS.2012.27.1.149
Printed March 1, 2012
Madjid Eshaghi Gordji, Norooz Ghobadipour, and Choonkil Park
Semnan University, Semnan University, Hanyang University
Abstract : In this paper, we prove the superstability and the generalized Hyers-Ulam stability of Jordan $*$-homomorphisms between unital $C^*$-algebras associated with the following functional equation $$f\left(\frac{-x+y}{3}\right)+f\left(\frac{x-3z}{3}\right)+f\left(\frac{3x-y+3z}{3}\right)=f(x).$$ Moreover, we investigate Jordan $*$-homomorphisms between unital $C^*$-algebras associated with the following functional inequality $$\left\|f\left(\frac{-x+y}{3}\right)+f\left(\frac{x-3z}{3}\right)+f\left(\frac{3x-y+3z}{3}\right)\right\| \leq \|f(x)\|.$$
Keywords : Jordan $*$-homomorphism, $C^*$-algebra, generalized Hyers-Ulam stability, functional equation and inequality
MSC numbers : Primary 17C65, 39B82, 46L05, 47Jxx, 47B48, 39B72
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