Original scientific paper

https://doi.org/10.3336/gm.46.1.07

Some remarks on derivations in semiprime rings and standard operator algebras

Joso Vukman ; Department of Mathematics and Computer Science, University of Maribor, FNM, Koroška 160, 2000 Maribor, Slovenia

Abstract

In this paper identities related to derivations on semiprime rings and standard operator algebras are investigated. We prove the following result which generalizes a classical result of Chernoff. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators of X into itself and let A(X) L(X) be a standard operator algebra. Suppose there exists a linear mapping D:A(X)→ L(X) satisfying the relation 2D(A3)=D(A2)A+A2D(A)+D(A)A2+AD(A2) for all A A(X). In this case D is of the form D(A)=AB-BA for all A A(X) and some fixed B L(X), which means that D is a linear derivation.

Keywords

Prime ring, semiprime ring; Banach space, standard operator algebra; derivation; Jordan derivation; Jordan triple derivation

Hrčak ID:

68874

URI

https://hrcak.srce.hr/68874

Publication date:

13.6.2011.

Visits: 1.263 *