
Journal of Lie Theory 15 (2005), No. 2, 393414 Copyright Heldermann Verlag 2005 Homomorphisms between Lie JC*Algebras and CauchyRassias Stability of Lie JC*Algebra Derivations ChunGil Park Dept. of Mathematics, Chungnam National University, Daejeon 305764, South Korea cgpark@cnu.ac.kr [Abstractpdf] It is shown that every almost linear mapping $h\colon A\rightarrow B$ of a unital Lie JC$^*$algebra $A$ to a unital Lie JC$^*$algebra $B$ is a Lie JC$^*$algebra homomorphism when $h(2^n u\circ y)=h(2^n u)\circ h(y)$, $h(3^n u\circ y)=h(3^n u)\circ h(y)$ or $h(q^n u\circ y)=h(q^n u)\circ h(y)$ for all $y\in A$, all unitary elements $u\in A$ and $n=0,1,2,\cdots$, and that every almost linear almost multiplicative mapping $h\colon A\rightarrow B$ is a Lie JC$^*$algebra homomorphism when $h(2x)=2h(x)$, $h(3x)=3h(x)$ or $h(qx)qh(x)$ for all $x\in A$. Here the numbers $2,3,q$ depend on the functional equations given in the almost linear mappings or in the almost linear almost multiplicative mappings. Moreover, we prove the CauchyRassias stability of Lie JC$^*$algebra homomorphisms in Lie JC$^*$algebras, and of Lie JC$^*$algebra derivations in Lie JC$^*$algebras. Keywords: Lie JC*algebra homomorphism, Lie JC*algebra derivation, stability, linear functional equation. MSC: 17B40, 39B52, 46L05; 17A36 [ Fulltextpdf (224 KB)] for subscribers only. 