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Approximate homomorphisms and derivations between \(C^*\)-ternary algebras. (English) Zbl 1152.81589
Summary: In 1940, Ulam proposed the famous Ulam stability problem. In this paper we introduce a general Cauchy-Jensen functional equation and prove the generalized Ulam stability of \(C^*\)-ternary homomorphisms and \(C^*\)-ternary derivations in \(C^*\)-ternary algebras for the general Cauchy-Jensen equation.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
46L99 Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.)
47B47 Commutators, derivations, elementary operators, etc.
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