Maps preserving Jordan triple product A*B+BA* on *-algebras
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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.
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.
참고문헌 (14)
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