Proper \(CQ^*\)-ternary algebras

Volume 7, Issue 4, pp 278--287 http://dx.doi.org/10.22436/jnsa.007.04.06

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Authors

Choonkil Park - Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea.

Abstract

In this paper, modifying the construction of a \(C^*\)-ternary algebra from a given \(C^*\)-algebra, we define a proper \(CQ^*\)-ternary algebra from a given proper \(CQ^*\)-algebra. We investigate homomorphisms in proper \(CQ^*\)-ternary algebras and derivations on proper \(CQ^*\)-ternary algebras associated with the Cauchy functional inequality \[\|f(x) + f(y) + f(z)\| \leq\| f(x + y + z)\|.\] We moreover prove the Hyers-Ulam stability of homomorphisms in proper \(CQ^*\)-ternary algebras and of derivations on proper \(CQ^*\)-ternary algebras associated with the Cauchy functional equation \[f(x + y + z) = f(x) + f(y) + f(z).\]

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Keywords

• proper \(CQ^*\)-ternary homomorphism
• proper \(CQ^*\)-ternary derivation
• Cauchy functional equation
• Hyers-Ulam stability.

MSC

•  47B48
•  39B72
•  47J05
•  39B52
•  17A40
•  47L60

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