Glasgow Mathematical Journal

Research Article

On the distance of the composition of two derivations to the generalized derivations

Matej Bresara1

a1 Institute of Mathematics, Physics and Mechanics, University of Ljubljana, P.O. Box 543, 61111 Ljubljana, Yugoslavia

A well-known theorem of E. Posner [10] states that if the composition d1 d2 of derivations d1 d2 of a prime ring A of characteristic not 2 is a derivation, then either d1 = 0 or d2 = 0. A number of authors have generalized this theorem in several ways (see e.g. [1], [2], and [5], where further references can be found). Under stronger assumptions when A is the algebra of all bounded linear operators on a Banach space (resp. Hilbert space), Posner's theorem was reproved in [3] (resp. [12]). Recently, M. Mathieu [8] extended Posner's theorem to arbitrary C*-algebras.