Isometric Isomorphisms in Proper CQ*-algebras

Abstract

In this paper, we prove the Hyers-Ulam-Rassias stability of isometric homomorphisms in proper CQ*-algebras for the following Cauchy-Jensen additive mapping: 2f(x(1) + x(2)/2 + y) = f(x(1)) + f(x(2)) + 2f(y). The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in the paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300. This is applied to investigate isometric isomorphisms between proper CQ*-algebras.