On Two-Sided Centralizers of Rings and Algebras

Abstract

In this paper we prove the following result. Let A be a semisimple H*−algebra and let T : A → A be an additive mapping satisfying the relation (n + 1)T(x^nm+1) = T(x)x^nm + x^mT(x)x^(n−1)m + · · · + x^nmT(x), for all x ∈ A and some fixed integers m ≥ 1, n ≥ 1. In this case T is a two-sided centralizer.