A NOTE ON NONLINEAR MIXED ∗-JORDAN TYPE DERIVATIONS ON ∗-ALGEBRAS | ||
| Journal of Algebraic Systems | ||
| دوره 13، شماره 1، تیر 2025، صفحه 177-190 اصل مقاله (133.57 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2023.12763.1691 | ||
| نویسندگان | ||
| Mohammad Aslam Siddeeque* ؛ Raof Ahmad Bhat؛ Abbas Hussain Shikeh | ||
| Department of Mathematics, Aligarh Muslim University, 202002, Aligarh, India. | ||
| چکیده | ||
| Let S be a ∗-algebra containing the unity and a nontrivial projection. In the present paper, we show that under certain restrictions if a map Ψ : S → S satisfies Ψ(L ⋄ N • D) = Ψ(L) ⋄ N • D + L ⋄Ψ(N) • D + L ⋄ N • Ψ(D) for all L, N, D ∈ S, then Ψ is an additive ∗-derivation. | ||
| کلیدواژهها | ||
| *-algebra؛ Mixed Jordan Triple derivation؛ *-derivation | ||
| مراجع | ||
|
1. L. Dai and F. Lu, Nonlinear maps preserving Jordan ∗-products, J. Math. Anal. Appl., 409(1) (2014), 180–188.
2. V. Darvish, H. M. Nazari, H. Rohi and A. Taghavi, Maps preserving η-product A∗B + ηBA∗ on C∗-algebras, J. Korean Math. Soc., 54(3) (2017), 867–876.
3. V. Darvish, M. Nouri and M. Razeghi, Nonlinear triple product A∗B+B∗A for derivations on ∗-algebras, Math. Notes, 108(1) (2020), 179–187.
4. D. Huo, B. Zheng, J. Xu and H. Liu, Nonlinear mappings preserving Jordan multiple ∗-product on factor von Neumann algebras, Linear Multilinear Algebra, 63(5) (2015), 1026–1036.
5. C. J. Li, Q. Y. Chen and T. Wang, Nonlinear maps preserving the Jordan triple ∗-product on factor von Neumann algebras, Chin. Ann. Math. Ser., 39(4) (2018), 633–642.
6. C. J. Li and F. Y. Lu, Nonlinear maps preserving the Jordan triple 1-∗-product on von Neumann algebras, Complex Anal. Oper. Theorey, 11(1) (2017), 109–117.
7. C. Li, F. Lu and X. Fang, Nonlinear ξ-Jordan ∗-derivation on von Neumann algebras, Linear Multilinear Algebra, 64(4) (2014), 466–472.
8. C. J. Li, F. Y. Lu and T. Wang, Nonlinear maps preserving the Jordan triple ∗-product on von Neumann algebras, Ann. Funct. Anal., 7(3) (2016), 496–507.
9. C. J. Li and D. Zhang, Nonlinear mixed Jordan triple ∗-derivations on ∗-algebras, Sib. Math. J., 63(4) (2022), 735–742.
10. C. J. Li, F. F. Zhao and Q. Y. Chen, Nonlinear skew Lie triple derivations between factors, Acta Math. Sin. (Engl. Ser.), 32(7) (2016), 821–830.
11. C. J. Li, Y. Zhao and F. F. Zhao, Nonlinear ∗-Jordan-type derivations on ∗-algebras, Rocky Mountain J. Math., 51(2) (2021), 601–612
12. Y. X. Liang and J. H. Zhang, Nonlinear mixed Lie triple derivable mappings on factor von Neumann algebras, Acta Math. Sinica (Chin. Ser.), 62(1) (2019), 13–24.
13. N. U. Rehman, J. Nisar and M. Nazim, A note on nonlinear mixed Jordan triple derivation on ∗-algebras, Comm. Algebra, (2022), 1–10.
14. A. Taghavi, M. Nouri, M. Razeghi and V. Darvish, Nonlinear λ-Jordan triple ∗- derivation on prime ∗-algebras, Rocky Mountain J. Math., 48(8) (2018), 2705–2716.
15. A. Taghavi, H. Rohi and V. Darvish, Non-linear ∗-Jordan derivation on von Neumann algebras, Linear Multilinear Algebra, 64 (2016), 426–439.
16. Z. J. Yang and J. H. Zhang, Nonlinear maps preserving mixed Lie triple products on factor von Neumann algebras, Ann. Funct. Anal., 10(3) (2019), 325–336.
17. F. J. Zhang, Nonlinear skew Jordan derivable maps on factor von Neumann algebras, Linear Multilinear Algebra, 64(10) (2016), 2090–2103.
18. F. F. Zhao and C. J. Li, Nonlinear ∗-Jordan triple derivations on von Neumann algebras, Math. Slovaca, 68(1) (2018), 163–170.
19. F. F. Zhao and C. J. Li, Nonlinear maps preserving the Jordan triple ∗-product between factors, Indag. Math., 29(2) (2017), 619–627.
20. Y. Zhou, Z. J. Yang and J. H. Zhang, Nonlinear mixed Lie triple derivations on prime ∗-algebras, Comm. Algebra, 47(1) (2019), 4791–4796. | ||
|
آمار تعداد مشاهده مقاله: 154 تعداد دریافت فایل اصل مقاله: 130 |
||