## Abstract

The purpose of this paper is to investigate identities with Jordan *-derivations in semiprime *-rings. Let ℛ be a 2-torsion free semiprime *-ring. In this paper it has been shown that, if *ℛ* admits an additive mapping *D* : *ℛ→ℛ*satisfying either *D*(*xyx*) = *D*(*xy*)*x ^{*}*+

*xyD*(

*x*) for all

*x,y*∈

*ℛ*, or

*D*(

*xyx*) =

*D*(

*x*)

*y*x**+

*xD*(

*yx*) for all pairs

*x, y*∈

*ℛ*, then

*D*is a

***-derivation. Moreover this result makes it possible to prove that if

*ℛ*satis es 2

*D*(

*x*) =

^{n}*D*(

*x*

^{n−}^{1})

*x*+

^{*}*x*

^{n−}^{1}

*D*(

*x*) +

*D*(

*x*)(

*x**)

^{n−}^{1}+

*xD*(

*x*

^{n−}^{1}) for all

*x*∈

*ℛ*and some xed integer

*n ≥*2, then

*D*is a Jordan

***-derivation under some torsion restrictions. Finally, we apply these purely ring theoretic results to standard operator algebras

*𝒜*(

*ℋ*). In particular, we prove that if

*ℋ*be a real or complex Hilbert space, with

*dim*(

*ℋ*)

*>*1, admitting a linear mapping

*D*:

*𝒜*(

*ℋ*)

*→ ℬ*(

*ℋ*) (where

*ℬ*(

*ℋ*) stands for the bounded linear operators) such that

for all *A*∈*𝒜*(*ℋ*). Then *D* is of the form *D*(*A*) = *AB−BA** for all *A*∈*𝒜*(*ℋ*) and some fixed *B* ∈ *ℬ*(*ℋ*), which means that *D* is Jordan ***-derivation.