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

Title & Authors
HOMOMORPHISMS BETWEEN C*-ALGEBRAS ASSOCIATED WITH THE TRIF FUNCTIONAL EQUATION AND LINEAR DERIVATIONS ON C*-ALGEBRAS
Park, Chun-Gil; Hou, Jin-Chuan;

Abstract
It is shown that every almost linear mapping h : A\longrightarrowB of a unital $\small{C^{*}}$ -algebra A to a unital $\small{C^{*}}$ -algebra B is a homomorphism under some condition on multiplication, and that every almost linear continuous mapping h : A\longrightarrowB of a unital $\small{C^{*}}$ -algebra A of real rank zero to a unital $\small{C^{*}}$ -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 $\small{C^{*}}$ -algebras, and of C-linear *-derivations on unital $\small{C^{*}}$ -algebras./ -algebras.
Keywords
homomorphism;C*-algebra of real rank zero;linear derivation;stability.;
Language
English
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