Stability of homomorphisms and derivations in $C^*$-ternary algebras

Details Stability of homomorphisms and derivations in $C^*$-ternary algebras Stability of homomorphisms and derivations in $C^*$-ternary algebras

2008-12-15

arxiv.org/abs/0812.2933v1

Mathematics

Operator Algebras

Scientific paper

In this paper, we investigate homomorphisms between $C^*$-ternary algebras and derivations on $C^*$-ternary algebras, associated with the following functional equation $$f(\frac{x_2-x_1}{3})+f(\frac{x_1-3x_3}{3})+f(\frac{3x_1+3x_3-x_2}{3})=f(x_1).$$ Moreover, we prove the generalized Hyers-Ulam -Rassias stability of homomorphisms in $C^*$-ternary algebras and of derivations on $C^*$-ternary algebras.

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