On Two-Sided Centralizers of Rings and Algebras

Joso Vukman; Irena Kosi-Ulbl

Authors

Joso Vukman Department of Mathematics and Computer Sciences, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroska 160, 2000 Maribor, Slovenia.
Irena Kosi-Ulbl Faculty of Education, University of Maribor, Koroska 160, 2000 Maribor, Slovenia.

Keywords:

Prime ring, semiprime ring, Banach space, standard operator algebra, ð»*-algebra, left (right) centralizer, left (right) Jordan centralizer, two-sided centralizer

Abstract

In this paper we prove the following result. Let A be a semisimple H*âˆ’algebra and let T : A â†’ A be an additive mapping satisfying the relation (n + 1)T(x^nm⁺¹) = T(x)x^nm + x^mT(x)x^(nâˆ’1)m + · · · + x^nmT(x), for all x âˆˆ A and some fixed integers m â‰¥ 1, n â‰¥ 1. In this case T is a two-sided centralizer.