Maps Preserving Strong Jordan Multiple *-Product on *-Algebras

کد مقاله : 1030-SLAA10

نویسندگان

علی تقوی * دانشکده علوم ریاضی

چکیده مقاله

\begin{abstract} Let $\mathcal{A}$ be an arbitrary $*$-algebra with unit I over the real or complex field $\mathbb{F} $ that contains a nontrivial idempotent $P_{1}$ and $ n\geq 1$ a natural number. Assume that $\varphi:\mathcal{A} \longrightarrow \mathcal{A}$ be a surjective map on $\mathcal{A}$ such that $\varphi$ satisfies condition \begin{center} $\varphi(P)\bullet_{n-1}\varphi(P)\bullet\varphi(A)=P\bullet_{n-1} P\bullet A$, \end{center} for every $ A \in\mathcal{A}$ and projection $P\in\{P_{1},~I-P_{1}\}$, where $ A\bullet_{n-1} A$ with repeat $ n-1 $ times $ A $ is the Jordan multiple $*$-product. Then $\varphi(A)=\varphi(I)A$ for all $ A\in\mathcal{A}$ and $\varphi(I)^2=I$. \end{abstract}

کلیدواژه ها

\abskeywords{Maps Preserving, Strong Jordan Multiple, $*$-Product.

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