Abstract and Applied Analysis
Volume 2008 (2008), Article ID 410437, 12 pages
doi:10.1155/2008/410437
Research Article

Jordan ∗-Derivations on C∗-Algebras and JC∗-Algebras

Jong Su An,1 Jianlian Cui,2 and Choonkil Park3

1Department of Mathematics Education, Pusan National University, Pusan 609-735, South Korea
2Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
3Department of Mathematics, Hanyang University, Seoul 133-791, South Korea

Received 19 September 2008; Revised 20 October 2008; Accepted 31 October 2008

Academic Editor: Ferhan Merdivenci Atici

Copyright © 2008 Jong Su An et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate Jordan ∗-derivations on C∗-algebras and Jordan ∗-derivations on JC∗-algebras associated with the following functional inequality ‖f(x)+f(y)+kf(z)‖≤‖kf((x+y)/k+z)‖ for some integer k greater than 1. We moreover prove the generalized Hyers-Ulam stability of Jordan ∗-derivations on C∗-algebras and of Jordan ∗-derivations on JC∗-algebras associated with the following functional equation f((x+y)/k+z)=(f(x)+f(y))/k+f(z) for some integer k greater than 1.