Abstract and Applied Analysis
Volume 2008 (2008), Article ID 410437, 12 pages
doi:10.1155/2008/410437
Jordan ∗-Derivations on C∗-Algebras and JC∗-Algebras
Jong Su An1
, Jianlian Cui2
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
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.