### Irena Kosi-Ulbl and Joso Vukman

Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia
e-mail: irena.kosi@um.si

Koroška cesta 57, 2000 Maribor, Slovenia
e-mail: joso.vukman@guest.um.si

Abstract.   In this paper we prove the following result. Let H be a real or complex Hilbert space, let L(H) be the algebra of all bounded linear operators on H and let A(H) ⊆ L(H) be a standard operator algebra. Suppose we have an additive mapping D:A(H) → L(H) satisfying the relation D(An)=D(A)A* n-1+AD(An-2)A* +An-1D(A) for all A A(H) and some fixed integer n>1. In this case there exists a unique B L(H) such that D(A)=BA*-AB holds for all A A(H).

2010 Mathematics Subject Classification.   16W10, 46K15, 39B05.

Key words and phrases.   Ring, ring with involution, prime ring, semiprime ring, Hilbert space, standard operator algebra, *-derivation, Jordan *-derivation.

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DOI: 10.3336/gm.50.2.07

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