additivity of maps preserving jordan $eta_{ast}$-products on $c^{*}$-algebras
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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 $ainmathcal{a}$ and $pin{p_{1},i_{mathcal{a}}-p_{1}}$ 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.
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Journal title:
bulletin of the iranian mathematical societyPublisher: iranian mathematical society (ims)
ISSN 1017-060X
volume 41
issue Issue 7 (Special Issue) 2015
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