Abstract and Applied Analysis

Nearly Jordan -Homomorphisms between Unital C -Algebras

A. Ebadian, S. Kaboli Gharetapeh, and M. Eshaghi Gordji

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Abstract

Let A , B be two unital C * -algebras. We prove that every almost unital almost linear mapping h : A B which satisfies h ( 3 n u y + 3 n y u ) = h ( 3 n u ) h ( y ) + h ( y ) h ( 3 n u ) for all u U ( A ) , all y A , and all n = 0 , 1 , 2 , , is a Jordan homomorphism. Also, for a unital C * -algebra A of real rank zero, every almost unital almost linear continuous mapping h : A B is a Jordan homomorphism when h ( 3 n u y + 3 n y u ) = h ( 3 n u ) h ( y ) + h ( y ) h ( 3 n u ) holds for all u I 1 ( A sa ), all y A , and all n = 0 , 1 , 2 , . Furthermore, we investigate the Hyers- Ulam-Aoki-Rassias stability of Jordan * -homomorphisms between unital C * -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

Permanent link to this document
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


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