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Maps preserving strong Jordan multiple $*$-product on $*$-algebras | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 21، دوره 13، شماره 2، مهر 2022، صفحه 221-225 اصل مقاله (292.74 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.19508.2083 | ||
| نویسنده | ||
| Ali Taghavi* | ||
| Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P. O. Box 47416-1468, Babolsar, Iran | ||
| تاریخ دریافت: 17 دی 1398، تاریخ بازنگری: 06 شهریور 1400، تاریخ پذیرش: 08 شهریور 1400 | ||
| چکیده | ||
| 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 and $\varphi:\mathcal{A} \longrightarrow \mathcal{A}$ be a surjective map on $\mathcal{A}$ such that $\varphi$ satisfies condition $$\varphi(P)\bullet_{n-1}\varphi(P)\bullet\varphi(A)=P\bullet_{n-1} P\bullet A,$$ 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 $\varphi(I)^2=I$. | ||
| کلیدواژه‌ها | ||
| Maps Preserving؛ Strong Jordan Multiple؛ $*$-Product | ||
| مراجع | ||
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