## 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.