Glasnik Matematicki, Vol. 46, No.1 (2011), 43-48.

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
e-mail: joso.vukman@uni-mb.si

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) in 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 in A(X). In this case D is of the form D(A)=AB-BA for all A in A(X) and some fixed B in L(X), which means that D is a linear derivation.

2000 Mathematics Subject Classification.   16W10, 46K15, 39B05.

Key words and phrases.   Prime ring, semiprime ring, Banach space, standard operator algebra, derivation, Jordan derivation, Jordan triple derivation.

Full text (PDF) (free access)

DOI: 10.3336/gm.46.1.07

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