@article { author = {Taghavi, A. and Rohi, H. and Darvish, V.}, title = {Additivity of maps preserving Jordan $\eta_{\ast}$-products on $C^{*}$-algebras}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {41}, number = {Issue 7 (Special Issue)}, pages = {107-116}, year = {2015}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {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.}, keywords = {Maps preserving Jordan $eta*$-product,Additive,Prime C*-algebras}, url = {http://bims.iranjournals.ir/article_726.html}, eprint = {http://bims.iranjournals.ir/article_726_46c90e129f3d8ce0cb2d465e7884246d.pdf} }