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Nonlinear $\ast $-derivation-type maps on sum of triple products on $\ast $-algebras | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 06 فروردین 1404 اصل مقاله (327.9 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.34391.5136 | ||
| نویسندگان | ||
| Joao Carlos da Motta Ferreira* ؛ Maria das Graças Bruno Marietto | ||
| Center for Mathematics, Computing and Cognition, Federal University of ABC, Avenida dos Estados, 5001, 09210-580, Santo Andre, Brazil | ||
| تاریخ دریافت: 20 خرداد 1403، تاریخ بازنگری: 05 شهریور 1403، تاریخ پذیرش: 19 شهریور 1403 | ||
| چکیده | ||
| Let $\mathcal{A}$ be a unital complex $\ast $-algebra having a nontrivial projection. In this paper, we proved that every $\ast $-derivation-type map $\Phi :\mathcal{A}\rightarrow \mathcal{A}$ on sum of triple products $\alpha _{1} abc+\alpha _{2} a^{*}cb^{*}+\alpha _{3} ba^{*}c +\alpha _{4} cab^{*}+\alpha _{5} bca+\alpha _{6} cb^{*}a^{*},$ where the scalars $\{\alpha _{k}\}_{k=1}^{6}$ are rational numbers satisfying some conditions, is an additive $\ast $-derivation. Some applications of the results obtained are also presented. | ||
| کلیدواژهها | ||
| Additive $\ast $-derivations؛ $\ast $-algebras؛ prime algebras؛ von Neumann algebras | ||
| مراجع | ||
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[1] L. Dai and F. Lu, Nonlinear maps preserving Jordan *-products, J. Math. Anal. Appl. 409 (2014), no. 1, 180–188. [2] V. Darvish, M. Nouri, M. Razeghi, and A. Taghavi, Nonlinear *-Jordan triple derivation on prime *-algebras, Rocky Mountain J. Math. 50 (2020), no. 2, 543–549. [3] J.C.M. Ferreira and M.G.B. Marietto, Nonlinear maps of *-derivation-type on a family of sum of triple products on *-algebras, Commun. Alg. 51 (2023), no. 8, 3394–3404. [4] N. Jacobson, Structure of Rings, vol. 37, American Mathematical Society Colloquium Publications, Providence, RI, 1956. [5] C. Li, F. Lu, and X. Fang, Nonlinear ξ-Jordan *-derivations on von Neumann algebras, Linear Multilinear Alg. 62 (2014), no. 4, 466–473. [6] C. Li and D. Zhang, Nonlinear mixed Jordan triple *-derivations on *-algebras, Sib. Math. J. 63 (2022), no. 4, 735–742. [7] C.J. Li, F.F. Zhao, and Q.Y. Chen, Nonlinear skew Lie triple derivations between factors, Acta. Math. Sin.-English Ser. 32 (2016), no. 7, 821–830. [8] C. Li, Y. Zhao, and F. Zhao, Nonlinear *-Jordan-type derivations on *-algebras, Rocky Mountain J. Math. 51 (2021), no. 2, 601–612. [9] L.H. Rowen, Ring Theory, Academic Press, San Diego, CA, 1991. [10] S¸.V. Stratila and L. Zsido, Lectures on von Neumann Algebras, Second Edition, Cambridge IISc Series, Cambridge University Press, 2019. | ||
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