Proper CQ*-ternary algebras

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 parallel to f(x) + f(y) + f(z)parallel to <= parallel to f(x + y + z)parallel to. 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).