# HOMOMORPHISMS BETWEEN C*-ALGEBRAS ASSOCIATED WITH THE TRIF FUNCTIONAL EQUATION AND LINEAR DERIVATIONS ON C*-ALGEBRAS

• Park, Chun-Gil (Department of Mathematics Chungnam National University) ;
• Hou, Jin-Chuan (Department of Mathematics Shanxi Teachers University, Department of Mathematics Shanxi University)
• Published : 2004.05.01

#### Abstract

It is shown that every almost linear mapping h : A\longrightarrowB of a unital $C^{*}$ -algebra A to a unital $C^{*}$ -algebra B is a homomorphism under some condition on multiplication, and that every almost linear continuous mapping h : A\longrightarrowB of a unital $C^{*}$ -algebra A of real rank zero to a unital $C^{*}$ -algebra B is a homomorphism under some condition on multiplication. Furthermore, we are going to prove the generalized Hyers-Ulam-Rassias stability of *-homomorphisms between unital $C^{*}$ -algebras, and of C-linear *-derivations on unital $C^{*}$ -algebras./ -algebras.

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