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

Published online by Cambridge University Press:  18 May 2009

Matej Bresar
Affiliation:
Institute of Mathematics, Physics and Mechanics, University of Ljubljana, P.O. Box 543, 61111 Ljubljana, Yugoslavia
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A well-known theorem of E. Posner [10] states that if the composition d1d2 of derivations d1d2 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.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

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