HYERS-ULAM-RASSIAS STABILITY OF ISOMORPHISMS IN C -ALGEBRAS

This paper is a survey on the Hyers–Ulam–Rassias stability of the Jensen functional equation in C ∗ -algebras. The concept of Hyers–Ulam–Rassias stability originated from the Th.M. Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300. Its content is divided into the following sections: 1. Introduction and preliminaries. 2. Approximate isomorphisms in C ∗ -algebras. 3. Approximate isomorphisms in Lie C ∗ -algebras. 4. Approximate isomorphisms in JC ∗ -algebras. 5. Stability of derivations on a C ∗ -algebra. 6. Stability of derivations on a Lie C ∗ -algebra. 7. Stability of derivations on a JC ∗ -algebra.