Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2012; 27(1): 149-158

Printed March 1, 2012

https://doi.org/10.4134/CKMS.2012.27.1.149

Copyright © The Korean Mathematical Society.

Jordan $*$-homomorphisms between unital $C^*$-algebras

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