Journal of Lie Theory

no. 2
Homomorphisms between Lie JC*-Algebras and Cauchy-Rassias Stability of Lie JC*-Algebra Derivations
Journal of Lie Theory, Volume 15 (2005) no. 2, pp. 393-414
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 Cauchy--Rassias stability of Lie JC$^*$-algebra homomorphisms in Lie JC$^*$-algebras, and of Lie JC$^*$-algebra derivations in Lie JC$^*$-algebras.
DOI: 10.5802/jolt.382
Classification: 17B40, 39B52, 46L05, 17A36
Keywords: Lie JC*-algebra homomorphism, Lie JC*-algebra derivation, stability, linear functional equation 
@article{JOLT_2005_15_2_a2,
     author = {C.-G. Park},
     title = {Homomorphisms between {Lie} {JC*-Algebras} and {Cauchy-Rassias} {Stability} of {Lie} {JC*-Algebra} {Derivations}},
     journal = {Journal of Lie Theory},
     pages = {393--414},
     year = {2005},
     volume = {15},
     number = {2},
     doi = {10.5802/jolt.382},
     zbl = {1091.39006},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.382/}
}
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%A C.-G. Park
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C.-G. Park. Homomorphisms between Lie JC*-Algebras and Cauchy-Rassias Stability of Lie JC*-Algebra Derivations. Journal of Lie Theory, Volume 15 (2005) no. 2, pp. 393-414. doi: 10.5802/jolt.382

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