Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P.O. Box 47416-1468, Babolsar, Iran.
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.
Taghavi, A., Rohi, H., & Darvish, V. (2015). Additivity of maps preserving Jordan $\eta_{\ast}$-products on $C^{*}$-algebras. Bulletin of the Iranian Mathematical Society, 41(Issue 7 (Special Issue)), 107-116.
MLA
A. Taghavi; H. Rohi; V. Darvish. "Additivity of maps preserving Jordan $\eta_{\ast}$-products on $C^{*}$-algebras". Bulletin of the Iranian Mathematical Society, 41, Issue 7 (Special Issue), 2015, 107-116.
HARVARD
Taghavi, A., Rohi, H., Darvish, V. (2015). 'Additivity of maps preserving Jordan $\eta_{\ast}$-products on $C^{*}$-algebras', Bulletin of the Iranian Mathematical Society, 41(Issue 7 (Special Issue)), pp. 107-116.
VANCOUVER
Taghavi, A., Rohi, H., Darvish, V. Additivity of maps preserving Jordan $\eta_{\ast}$-products on $C^{*}$-algebras. Bulletin of the Iranian Mathematical Society, 2015; 41(Issue 7 (Special Issue)): 107-116.
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