TY - JOUR ID - 726 TI - Additivity of maps preserving Jordan $\eta_{\ast}$-products on $C^{*}$-algebras JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Taghavi, A. AU - Rohi, H. AU - Darvish, V. AD - Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P.O. Box 47416-1468, Babolsar, Iran. Y1 - 2015 PY - 2015 VL - 41 IS - Issue 7 (Special Issue) SP - 107 EP - 116 KW - Maps preserving Jordan $eta*$-product KW - Additive KW - Prime C*-algebras DO - N2 - 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. UR - http://bims.iranjournals.ir/article_726.html L1 - http://bims.iranjournals.ir/article_726_46c90e129f3d8ce0cb2d465e7884246d.pdf ER -