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http://dx.doi.org/10.11568/kjm.2018.26.1.61

MAPS PRESERVING JORDAN TRIPLE PRODUCT A*B + BA* ON *-ALGEBRAS  

Taghavi, Ali (Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran)
Nouri, Mojtaba (Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran)
Razeghi, Mehran (Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran)
Darvish, Vahid (Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran)
Publication Information
Korean Journal of Mathematics / v.26, no.1, 2018 , pp. 61-74 More about this Journal
Abstract
Let $\mathcal{A}$ and $\mathcal{B}$ be two prime ${\ast}$-algebras. Let ${\Phi}:\mathcal{A}{\rightarrow}\mathcal{B}$ be a bijective and satisfies $${\Phi}(A{\bullet}B{\bullet}A)={\Phi}(A){\bullet}{\Phi}(B){\bullet}{\Phi}(A)$$, for all $A,B{\in}{\mathcal{A}}$ where $A{\bullet}B=A^{\ast}B+BA^{\ast}$. Then, ${\Phi}$ is additive. Moreover, if ${\Phi}(I)$ is idempotent then we show that ${\Phi}$ is ${\mathbb{R}}$-linear ${\ast}$-isomorphism.
Keywords
Jordan triple product; ${\ast}$-isomorphism; Prime ${\ast}$-algebras;
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Times Cited By KSCI : 1  (Citation Analysis)
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