## Abstract and Applied Analysis

### Nearly Jordan $∗$-Homomorphisms between Unital $C ∗$-Algebras

#### Abstract

Let $A$, $B$ be two unital ${C}^{\ast }$-algebras. We prove that every almost unital almost linear mapping $h$ : $A\to B$ which satisfies $h({3}^{n}uy+{3}^{n}yu)=h({3}^{n}u)h(y)+h(y)h({3}^{n}u)$ for all $u\in U(A)$, all $y\in A$, and all $n=0,1,2,\dots$, is a Jordan homomorphism. Also, for a unital ${C}^{\ast }$-algebra $A$ of real rank zero, every almost unital almost linear continuous mapping $h:A\to B$ is a Jordan homomorphism when $h({3}^{n}uy+{3}^{n}yu)=h({3}^{n}u)h(y)+h(y)h({3}^{n}u)$ holds for all $u\in {I}_{1}$ (${A}_{\text{sa}}$), all $y\in A$, and all $n=0,1,2,\dots$. Furthermore, we investigate the Hyers- Ulam-Aoki-Rassias stability of Jordan $\ast$-homomorphisms between unital ${C}^{\ast }$-algebras by using the fixed points methods.

#### Article information

Source
Abstr. Appl. Anal., Volume 2011 (2011), Article ID 513128, 12 pages.

Dates
First available in Project Euclid: 12 August 2011

https://projecteuclid.org/euclid.aaa/1313171168

Digital Object Identifier
doi:10.1155/2011/513128

Mathematical Reviews number (MathSciNet)
MR2800073

Zentralblatt MATH identifier
1223.39015

#### Citation

Ebadian, A.; Gharetapeh, S. Kaboli; Gordji, M. Eshaghi. Nearly Jordan ∗ -Homomorphisms between Unital C ∗ -Algebras. Abstr. Appl. Anal. 2011 (2011), Article ID 513128, 12 pages. doi:10.1155/2011/513128. https://projecteuclid.org/euclid.aaa/1313171168