%0 Journal Article %T Additivity of maps preserving Jordan $\eta_{\ast}$-products on $C^{*}$-algebras %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Taghavi, A. %A Rohi, H. %A Darvish, V. %D 2015 %\ 12/01/2015 %V 41 %N Issue 7 (Special Issue) %P 107-116 %! Additivity of maps preserving Jordan $\eta_{\ast}$-products on $C^{*}$-algebras %K Maps preserving Jordan $eta*$-product %K Additive %K Prime C*-algebras %R %X Let $\mathcal{A}$ and $\mathcal{B}$ be two $C^{*}$-algebras such that $\mathcal{B}$ is prime. In this paper, we investigate the additivity of maps $\Phi$ from $\mathcal{A}$ onto $\mathcal{B}$ that are bijective, unital and satisfy $\Phi(AP+\eta PA^{*})=\Phi(A)\Phi(P)+\eta \Phi(P)\Phi(A)^{*},$ for all $A\in\mathcal{A}$ and $P\in\{P_{1},I_{\mathcal{A}}-P_{1}\}$ where $P_{1}$ is a nontrivial projection in $\mathcal{A}$. If $\eta$ is a non-zero complex number such that $|\eta|\neq1$, then $\Phi$ is additive. Moreover, if $\eta$ is rational<,> then $\Phi$ is $\ast$-additive. %U http://bims.iranjournals.ir/article_726_46c90e129f3d8ce0cb2d465e7884246d.pdf