Korean J. Math. Vol. 26 No. 1 (2018) pp.61-74
DOI: https://doi.org/10.11568/kjm.2018.26.1.61

Maps preserving Jordan triple product $A^{*}B+BA^{*}$ on $\ast$-algebras

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Published: Mar 30, 2018
Keywords:
Jordan triple product, $\ast$-isomorphism, Prime $\ast$-algebras
Mathematics Subject Classification:
47B48, 46L10

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Ali Taghavi
Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran, P. O. Box 47416-1468 Babolsar, Iran.
Mojtaba Nouri
Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran, P. O. Box 47416-1468 Babolsar, Iran.
Mehran Razeghi
Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran, P. O. Box 47416-1468 Babolsar, Iran.
Vahid Darvish
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 prime $\ast$-algebras. Let $\Phi: \mathcal{A}\to \mathcal{B}$ 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 $A\bullet B=A^{*}B+BA^{*}$. 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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