Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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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)
  • Received : 2018.01.26
  • Accepted : 2018.03.16
  • Published : 2018.03.30
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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.

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References

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