Proper $CQ^*$-ternary algebras

Park, Choonkil¹

¹ Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea

Journal of nonlinear sciences and its applications, Tome 7 (2014) no. 4, p. 278-287.

Résumé

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

$f(x + y + z) = f(x) + f(y) + f(z).$

Détail

DOI : 10.22436/jnsa.007.04.06

Classification : 47B48, 39B72, 47J05, 39B52, 17A40, 47L60
Keywords: proper \(CQ^*\)-ternary homomorphism, proper \(CQ^*\)-ternary derivation, Cauchy functional equation, Hyers-Ulam stability.

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