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http://dx.doi.org/10.4134/JKMS.j160286

MAPS PRESERVING η-PRODUCT A⁎B+ηBA⁎ ON C⁎-ALGEBRAS  

Darvish, Vahid (Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran)
Nazari, Haji Mohammad (Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran)
Rohi, Hamid (Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran)
Taghavi, Ali (Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran)
Publication Information
Journal of the Korean Mathematical Society / v.54, no.3, 2017 , pp. 867-876 More about this Journal
Abstract
Let $\mathcal{A}$ and $\mathcal{B}$ be two $C^*$-algebras such that $\mathcal{A}$ is prime. In this paper, we investigate the additivity of maps ${\Phi}$ from $\mathcal{A}$ onto $\mathcal{B}$ that are bijective and satisfy $${\Phi}(A^*B+{\eta}BA^*)={\Phi}(A)^*{\Phi}(B)+{\eta}{\Phi}(B){\Phi}(A)^*$$ for all $A,B{\in}\mathcal{A}$ where ${\eta}$ is a non-zero scalar such that ${\eta}{\neq}{\pm}1$. Moreover, if ${\Phi}(I)$ is a projection, then ${\Phi}$ is a ${\ast}$-isomorphism.
Keywords
maps preserving ${\eta}$-product; ${\ast}$-isomorphism; prime $C^*$-algebras;
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