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

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

Ali Taghavi, Mojtaba Nouri, Mehran Razeghi, Vahid Darvish

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.

Keywords


Jordan triple product, $\ast$-isomorphism, Prime $\ast$-algebras

Subject classification

47B48, 46L10

Sponsor(s)



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